{"group":{"group":{"id":60265,"name":"Easy Sequences Volume VIII","lockable":false,"created_at":"2023-01-24T09:59:54.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Collection of math challenges. Not necessarily easy and not necessarily about sequences...","is_default":false,"created_by":255988,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":5749,"published":true,"community_created":true,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCollection of math challenges. Not necessarily easy and not necessarily about sequences...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 289.5px 21px; transform-origin: 289.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 266.5px 21px; text-align: left; transform-origin: 266.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247px 8px; transform-origin: 247px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCollection of math challenges. Not necessarily easy and not necessarily about sequences...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2023-05-15T09:49:21.000Z"},"current_player":null},"problems":[{"id":53735,"title":"Easy Sequences 58: Curious Prime-Rational Functions","description":"For some prime numbers  and  where , a rational function , is defined as follows: .   Using the output , another rational function , is defined: .   Finaly, using the output , we define the function : ;  where the symbol \"\", represents the integer part of the decimal expansion of the fraction  .\r\nFor example for  and : ; ; since , .\r\nAnd, for  and : ; ; since, .\r\nIf , and given an integer limit , write a function that returns a sorted array of all unique values of  that are less than or equal to .\r\n-----------\r\nHINT:     Both  and , are rational functions and expect exact rational fraction outputs. Therefore, please preserve numerators and denominators for  and , and evaluate decimal expansions only when calculating the output of the function . 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height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.5px 8px; transform-origin: 62.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, a rational function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71px 8px; transform-origin: 71px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is defined as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 165px; height: 35px;\" width=\"165\" height=\"35\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.   Using the output \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 72.5px; height: 18.5px;\" width=\"72.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83px 8px; transform-origin: 83px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, another rational function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is defined: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 94.5px; height: 35px;\" width=\"94.5\" height=\"35\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.   Finaly, using the output \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 58.5px; height: 18.5px;\" width=\"58.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we define the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-14px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 129px; height: 39.5px;\" width=\"129\" height=\"39.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.5px 8px; transform-origin: 65.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;  where the symbol \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAlCAYAAADSvLDKAAAAh0lEQVRYhe3YwQmDQBgF4enBDtKADViBFaQDO7CmlGAx9hIPelqSwMNfhDADy96eH3sUzC5pBB43fLOrGFqAuWIoaAWGiqE78G/Ei48TD+LjxIP4OPEgPk48iI8TD+LjxIP4OPEgPk48/AF+Pe72PE9uv77sluFH9pf/dPqT29OP7ZK/xGZNG+TqVZ2JawLPAAAAAElFTkSuQmCC\" style=\"width: 23.5px; height: 18.5px;\" width=\"23.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 139px 8px; transform-origin: 139px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\", represents the integer part of the decimal expansion of the fraction \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 28px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 14px; text-align: left; transform-origin: 384px 14px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 99.5px; height: 28px;\" width=\"99.5\" height=\"28\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 95.5px; height: 28px;\" width=\"95.5\" height=\"28\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; since \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 49px; height: 18.5px;\" width=\"49\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 81px; height: 18.5px;\" width=\"81\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 28px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 14px; text-align: left; transform-origin: 384px 14px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAnd, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 99.5px; height: 28px;\" width=\"99.5\" height=\"28\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 95.5px; height: 28px;\" width=\"95.5\" height=\"28\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.5px 8px; transform-origin: 20.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; since\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 49px; height: 18.5px;\" width=\"49\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 73.5px; height: 18.5px;\" width=\"73.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 60px; height: 18.5px;\" width=\"60\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, and given an integer limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 173.5px 8px; transform-origin: 173.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, write a function that returns a sorted array of all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.5px 8px; transform-origin: 24.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eunique\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.5px 8px; transform-origin: 36.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e that are less than or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.5px 8px; transform-origin: 27.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-----------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHINT:     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.5px 8px; transform-origin: 16.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBoth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109px 8px; transform-origin: 109px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, are rational functions and expect \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.5px 8px; transform-origin: 16.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eexact\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169px 8px; transform-origin: 169px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rational fraction outputs. Therefore, please preserve numerators and denominators for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and evaluate decimal expansions only when calculating the output of the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ns = arrayNs(x)\r\n    ns = 1:x;\r\nend","test_suite":"%%\r\nx = 1e2;\r\nns_correct = [0 19 28 78];\r\nassert(isequal(arrayNs(x),ns_correct))\r\n%%\r\nx = 1e3;\r\nns_correct = [0 19 28 78 166 622];\r\nassert(isequal(arrayNs(x),ns_correct))\r\n%%\r\nx = 1e4;\r\nns_correct = [0 19 28 78 166 622 1366 3718 7222];\r\nassert(isequal(arrayNs(x),ns_correct))\r\n%%\r\nx = 1e6;\r\nns = arrayNs(x);\r\nss = [length(ns) sum(ns) sum(num2str(ns))];\r\nss_correct = [27 4981111 9249];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nx = 1e8;\r\nns = arrayNs(x);\r\nss = [length(ns) sum(ns) sum(num2str(ns))];\r\nss_correct = [129 3617934043 59547];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nx = intmax;\r\nns = arrayNs(x);\r\nss = [length(ns) sum(ns) sum(num2str(ns))];\r\nss_correct = [394 241721655665 219718];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nx = 1e10;\r\nns = arrayNs(x);\r\nss = [length(ns) sum(ns) sum(num2str(ns))];\r\nss_correct = [708 1999864114957 404552];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nx = 1e12;\r\nns = arrayNs(x);\r\nss = [length(ns) sum(ns) sum(num2str(ns))];\r\nss_correct = [4568 1322484296840565 3099611];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nx = flintmax;\r\nns = arrayNs(x);\r\nss = [length(ns) sum(num2str(ns))];\r\nss_correct = [228372 203164785];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('arrayNs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-12-21T18:52:30.000Z","updated_at":"2026-03-26T12:27:50.000Z","published_at":"2021-12-22T07:55:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor some prime numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \u0026lt; q\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, a rational function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(p,q)=\\\\frac{2pq+p+q+1}{pq+q} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.   Using the output \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er = R(p,q)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, another rational function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK(r)\\\\  =\\\\  \\\\frac{2r}{2-r} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.   Finaly, using the output \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek=K(r)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we define the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN(k)=\\\\begin{cases}k\u0026amp;\\\\left\\\\lfloor k\\\\right\\\\rfloor  =k\\\\\\\\ 0\u0026amp;\\\\left\\\\lfloor k\\\\right\\\\rfloor  \\\\neq k\\\\end{cases} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e;  where the symbol \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left\\\\lfloor \\\\ \\\\right\\\\rfloor  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\", represents the integer part of the decimal expansion of the fraction \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er=R(2,5)= \\\\frac_{28}_{15}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek=K(\\\\frac_{28}_{15})=28\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left\\\\lfloor k\\\\right\\\\rfloor  = k\\\\end\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\therefore N(k)=28\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnd, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq=7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er=R(3,7)= \\\\frac_{53}_{28}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek=K(\\\\frac_{53}_{28})= \\\\frac_{106}_{3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; since\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left\\\\lfloor k\\\\right\\\\rfloor  \\\\neq k\\\\end\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\therefore N(k)=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=N(k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, and given an integer limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that returns a sorted array of all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunique\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e that are less than or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-----------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHINT:     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eBoth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, are rational functions and expect \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexact\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e rational fraction outputs. Therefore, please preserve numerators and denominators for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and evaluate decimal expansions only when calculating the output of the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53755,"title":"Easy Sequence 61: Wide Pythagorean Triangles","description":"An integer-sided right triangle with sides , is called a \"wide Pythagorean triangle\", if , and . \r\nWrite a program that counts all wide Pythagorean triangles whose no sides greater than a given limit .\r\nBelow is the list of all Pythagorean triangles with all sides :\r\n    \r\nTherefore, for , your program output should be . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 222.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 111.25px; transform-origin: 407px 111.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128px 8px; transform-origin: 128px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn integer-sided right triangle with sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 47.5px; height: 18.5px;\" width=\"47.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134px 8px; transform-origin: 134px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is called a \"wide Pythagorean triangle\", if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 61px; height: 18px;\" width=\"61\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 60px; height: 18px;\" width=\"60\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 354px 8px; transform-origin: 354px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a program that counts all wide Pythagorean triangles whose no sides greater than a given limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003es\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 180px 8px; transform-origin: 180px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBelow is the list of all Pythagorean triangles with all sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 40px; height: 18px;\" width=\"40\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 102.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 51.25px; text-align: left; transform-origin: 384px 51.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-45px\"\u003e\u003cimg 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\" style=\"width: 745px; height: 102.5px;\" width=\"745\" height=\"102.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 50px; height: 18px;\" width=\"50\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, your program output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = countWPTs(s)\r\n    c = length(primes(s)) + 20;\r\nend","test_suite":"%%\r\ns = 100;\r\nc_correct = 45;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 300;\r\nc_correct = 196;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 1000;\r\nc_correct = 857;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 10000;\r\nc_correct = 12397;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 100000;\r\nc_correct = 161208;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 1000000;\r\nc_correct = 1979930;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 10000000;\r\nc_correct = 23469232;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 100000000;\r\nc_correct = 271353574;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\nss = floor((pi/2) .^ (11:40));\r\ncs = arrayfun(@(s) countWPTs(s),ss);\r\nss = [sum(cs) nnz(find(cs)) floor(std(ss)) sum(num2str(cs))];\r\nss_correct = [487155754 30 15528091 13675];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('countWPTs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-05T05:25:43.000Z","updated_at":"2025-11-21T18:31:53.000Z","published_at":"2022-01-05T08:26:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn integer-sided right triangle with sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[a,b,c]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is called a \\\"wide Pythagorean triangle\\\", if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb \\\\ge a+2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec \\\\ge b+2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a program that counts all wide Pythagorean triangles whose no sides greater than a given limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBelow is the list of all Pythagorean triangles with all sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{ \\\\ [6,8,10],\\\\ [9,12,15],\\\\ [8,15,17],\\\\ [12,16,20],\\\\ [15,20,25],\\\\ [10,24,26],\\\\ [18,24,30],\\\\ [16,30,34],\\\\ [21,28,35],\\\\ \\\\\\\\\\n\\\\ \\\\ [12,35,37],\\\\ [15,36,39],\\\\ [24,32,40],\\\\ [27,36,45],\\\\ [30,40,50],\\\\ [14,48,50],\\\\ [24,45,51],\\\\ [20,48,52],\\\\ [28,45,53],\\\\ \\\\\\\\\\n\\\\ \\\\ [33,44,55],\\\\ [40,42,58],\\\\ [36,48,60],\\\\ [39,52,65],\\\\ [25,60,65],\\\\ [16,63,65],\\\\ [33,56,65],\\\\ [32,60,68],\\\\ [42,56,70],\\\\ \\\\\\\\\\n\\\\ \\\\ [48,55,73],\\\\ [24,70,74],\\\\ [45,60,75],\\\\ [21,72,75],\\\\ [30,72,78],\\\\ [48,64,80],\\\\ [18,80,82],\\\\ [51,68,85],\\\\ [40,75,85],\\\\ \\\\\\\\\\n\\\\ \\\\ [36,77,85],\\\\ [60,63,87],\\\\ [39,80,89],\\\\ [54,72,90],\\\\ [35,84,91],\\\\ [57,76,95],\\\\ [62,72,97],\\\\ [60,80,100],\\\\ [28,96,100]\\\\ \\\\}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, your program output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e45\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53760,"title":"Easy Sequences 62: Sum of Omega-3 Function","description":"For an integer , the prime big omega function, , is defined as the total number of prime factors of . If  , since , therefore . The omega-3 function (), is defined as raising  to the power of the prime big omega of , i.e. . In the example above, .\r\nGiven an integer , write a function that returns the sum of omega-3's of all integers from  to . For example for  the function output should be , since:\r\n             ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 277px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Prime_omega_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eprime big omega\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"19\" style=\"width: 33.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, is defined as the total number of prime factors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. If  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"51.5\" height=\"18\" style=\"width: 51.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, since \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"103.5\" height=\"19\" style=\"width: 103.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, therefore \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"149.5\" height=\"19\" style=\"width: 149.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. The omega-3 function (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38.5\" height=\"20\" style=\"width: 38.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e), is defined as raising \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e3\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e to the power of the prime big omega of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, i.e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"84.5\" height=\"21\" style=\"width: 84.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. In the example above, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"125.5\" height=\"21\" style=\"width: 125.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, write a function that returns the sum of omega-3's of all integers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e For example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e the function output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, since:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 133px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-50px\"\u003e\u003cimg 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\" width=\"621.5\" height=\"112\" style=\"width: 621.5px; height: 112px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = sumOmega3(n)\r\n    s = 3 / 4 * n * 10 + 1;\r\nend","test_suite":"%%\r\nn = 10;\r\ns_correct = 76;\r\nassert(isequal(sumOmega3(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 4378;\r\nassert(isequal(sumOmega3(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 183286;\r\nassert(isequal(sumOmega3(n),s_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 8669878;\r\nassert(isequal(sumOmega3(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 350459176;\r\nassert(isequal(sumOmega3(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 12473731018;\r\nassert(isequal(sumOmega3(n),s_correct))\r\n%%\r\nn = 10000000;\r\ns_correct = 532877453914;\r\nassert(isequal(sumOmega3(n),s_correct))\r\n%%\r\nns = 2.^(7:27);\r\nss = arrayfun(@(n) sumOmega3(n),ns);\r\nassert(isequal([54168978173730 length(ss) 14288 8148263610388],[sum(ss) sum(mod(ss,3)) sum(num2str(ss)) floor(std(ss))]));\r\n%%\r\nfiletext = fileread('sumOmega3.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-06T04:57:22.000Z","updated_at":"2026-03-26T12:58:13.000Z","published_at":"2022-01-07T15:17:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Prime_omega_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eprime big omega\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Omega(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined as the total number of prime factors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=300\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e300 = 2^2\\\\cdot3^1\\\\cdot5^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Omega(300) = 2 + 1 + 2 =5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The omega-3 function (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Omega_{3}(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), is defined as raising \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to the power of the prime big omega of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, i.e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Omega_{3}(n) = 3^{\\\\Omega(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. In the example above, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Omega_{3}(300) = 3^5 = 243\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that returns the sum of omega-3's of all integers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e For example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the function output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e76\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, since:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sum_{i=1}^{10}  \\\\Omega_{3}(i) = \\\\Omega_{3}(1)+\\\\Omega_{3}(2)+\\\\Omega_{3}(3)+\\\\Omega_{3}(4)+\\\\Omega_{3}(5)+\\\\Omega_{3}(6)+\\\\Omega_{3}(7)+\\\\Omega_{3}(8)+\\\\Omega_{3}(9)+\\\\Omega_{3}(10)\\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ = \\\\ 3^{\\\\Omega(1)} + 3^{\\\\Omega(2)} + 3^{\\\\Omega(3)} + 3^{\\\\Omega(4)} + 3^{\\\\Omega(5)} + 3^{\\\\Omega(6)} + 3^{\\\\Omega(7)} + 3^{\\\\Omega(8)} + 3^{\\\\Omega(9)} + 3^{\\\\Omega(10)}\\\\\\\\\\n\\\\ \\\\ \\\\ \\\\  \\\\ \\\\ \\\\ \\\\ = \\\\ 3^{0} + 3^{1} + 3^{1} + 3^{2} + 3^{1} + 3^{2} + 3^{1} + 3^{3} + 3^{2} + 3^{2}\\\\ = \\\\ 1 + 3 + 3 + 9 + 3 + 9  + 3 + 27 + 9  + 9\\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ = \\\\ 76\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53750,"title":"Easy Sequences 63: Base-63 Arithmetic Functions","description":"In this exercise we are required to implement 7 basic 'unsigned integer' arithmetic functions in base-63:\r\n    to63(x) - converts an integer from base-10 to base-63.\r\n    to10(x) - converts an integer from base-63 to base-10.\r\n    add(x,y) - adds  two base-63 integers.\r\n    sub(x,y) - subtracts two base-63 integers.\r\n    mul(x,y) - multiplies  two base-63 integers.\r\n    div(x,y) - performs integer division between two base-63 integers.\r\n    mod(x,y) - returns the remainder of division between two base-63 integers.\r\nNOTES:\r\nAll outputs shall be char-string format.\r\nExcept for the function 'to63' (which may input numbers), all inputs shall be in char-string format.\r\nUse the numerals '0' to '9' for digits 0 to 9, capital letters 'A' to 'Z' for digits 10 to 35, lower case letters 'a' to 'z' for digits 36 to 61 and the symbol '_' (underscore) for digit 62.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 306.767px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 153.383px; transform-origin: 407px 153.383px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108px 8px; transform-origin: 108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this exercise we are required to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 238.5px 8px; transform-origin: 238.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eimplement 7 basic 'unsigned integer' arithmetic functions in base-63\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 143.033px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 71.5167px; transform-origin: 391px 71.5167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 179.5px 8px; transform-origin: 179.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    to63(x) - converts an integer from base-10 to base-63.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 179.5px 8px; transform-origin: 179.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    to10(x) - converts an integer from base-63 to base-10.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 127.5px 8px; transform-origin: 127.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    add(x,y) - adds  two base-63 integers.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 138.5px 8px; transform-origin: 138.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    sub(x,y) - subtracts two base-63 integers.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 140px 8px; transform-origin: 140px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    mul(x,y) - multiplies  two base-63 integers.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 213px 8px; transform-origin: 213px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    div(x,y) - performs integer division between two base-63 integers.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 242px 8px; transform-origin: 242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    mod(x,y) - returns the remainder of division between two base-63 integers.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.5px 8px; transform-origin: 25.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTES:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 119.5px 8px; transform-origin: 119.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAll outputs shall be char-string format.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 302px 8px; transform-origin: 302px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExcept for the function 'to63' (which may input numbers), all inputs shall be in char-string format.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 356px 8px; transform-origin: 356px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUse the numerals '0' to '9' for digits 0 to 9, capital letters 'A' to 'Z' for digits 10 to 35, lower case letters 'a' to 'z' for digits 36 to 61 and the symbol '_' (underscore) for digit 62.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b63 = Base63()\r\n    to63(x) = dec2base(x,63);\r\n    to10(x) = base2dec(x,63);\r\n    add(x,y) = x + y;\r\n    sub(x,y) = x - y;\r\n    mul(x,y) = x * y;\r\n    div(x,y) = floor(x/y);\r\n    mod(x,y) = mod(x,y);\r\nend","test_suite":"%%\r\nx = 123456789101112;\r\nz_correct = 'VLZfwM1X';\r\nassert(isequal(Base63().to63(x),z_correct))\r\n\r\nx = '1234567891011121314151617181920';\r\nz_correct = 'K30d4dXd8FooeXzgC';\r\nassert(isequal(Base63().to63(x),z_correct))\r\n \r\nx = '_____________';\r\nz_correct = '246278864694166156419902';\r\nassert(isequal(Base63().to10(x),z_correct))\r\n\r\nx = '12345ABCDE';\r\ny = 'abc_123_';\r\nz_correct = '12dfi9CEHD';\r\nassert(isequal(Base63().add(x,y),z_correct))\r\n\r\nx = 'AaAaAaAaAaAaAa';\r\ny = 'zzzzzzzzzz';\r\nz_correct = 'AaAZBbBbBbBbBc';\r\nassert(isequal(Base63().sub(x,y),z_correct))\r\n\r\nx = 'AaAaAaAaAaAaAa';\r\ny = '_zzzzzzzzzz_';\r\nz_correct = 'AZ_qG5WLmc1sII7jIT2CmxWhGR';\r\nassert(isequal(Base63().mul(x,y),z_correct))\r\n\r\nx = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ';\r\ny = '1234567890abcd';\r\nz_correct = '9s0000001Scv0';\r\nassert(isequal(Base63().div(x,y),z_correct))\r\n\r\nx = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ';\r\ny = '1234567890abcd';\r\nz_correct = '6Moq3p6Yvs4GZ';\r\nassert(isequal(Base63().mod(x,y),z_correct))\r\n\r\n%%\r\nx = randi(1000000000);\r\ny = randi(1000000);\r\nassert(isequal(Base63().add(Base63().to63(x),Base63().to63(y)),Base63().to63(x+y)))\r\nassert(isequal(Base63().sub(Base63().to63(x),Base63().to63(y)),Base63().to63(x-y)))\r\nassert(isequal(Base63().mul(Base63().to63(x),Base63().to63(y)),Base63().to63(x*y)))\r\nassert(isequal(Base63().div(Base63().to63(x),Base63().to63(y)),Base63().to63(floor(x/y))))\r\nassert(isequal(Base63().mod(Base63().to63(x),Base63().to63(y)),Base63().to63(mod(x,y))))\r\n\r\nx = '12345678910ABCDEFGHIJKLMNOPQRSTUVWXYZ';\r\ny = '_zyxwvutsrqponmlkjihgfedcba__';\r\nt = [Base63().add(x,y) Base63().sub(x,y) Base63().mul(x,y) Base63().div(x,y) Base63().mod(x,y)];\r\nh = histc(t,unique(t));\r\ns = [length(t) sum(t) length(h) str2num(Base63().to10(t(1:20:end)))];\r\ns_correct = [sum(h) 13812 58 276016002735090];\r\nassert(isequal(s,s_correct))\r\n\r\n\r\n%%\r\nfiletext = fileread('Base63.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-03T12:31:43.000Z","updated_at":"2026-03-26T13:37:03.000Z","published_at":"2022-01-13T06:50:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this exercise we are required to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eimplement 7 basic 'unsigned integer' arithmetic functions in base-63\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    to63(x) - converts an integer from base-10 to base-63.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    to10(x) - converts an integer from base-63 to base-10.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    add(x,y) - adds  two base-63 integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    sub(x,y) - subtracts two base-63 integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    mul(x,y) - multiplies  two base-63 integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    div(x,y) - performs integer division between two base-63 integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    mod(x,y) - returns the remainder of division between two base-63 integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTES:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll outputs shall be char-string format.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExcept for the function 'to63' (which may input numbers), all inputs shall be in char-string format.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the numerals '0' to '9' for digits 0 to 9, capital letters 'A' to 'Z' for digits 10 to 35, lower case letters 'a' to 'z' for digits 36 to 61 and the symbol '_' (underscore) for digit 62.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53905,"title":"Easy Sequences 64: Base-14 Arithmetic Function","description":"For an integer , the base-14 arithmetic function, , is defined as follows:\r\nConvert  to base-14, using the letters '' for digits  to .\r\nReplace the letters '' with the arithmetic operation symbols '', respectively.\r\nRemove any leading or trailing operation symbols.\r\nFor consecutive operation symbols between two numeric symbols, retain only the first operation and remove all others.\r\nEvaluate the resulting expression in base-10.\r\nReturn the evaluated expression as , rounded-off to the nearest integer.\r\nFinally, output  if  contains only \"operation symbols\", or if , or if , or if .\r\nFor example if :\r\n        \r\nTherefore:\r\n        .\r\nGiven a set positive integers , find the integer , , such that  is minimized. If there are more than one integers,  in  that minimizes , please output the largest of those 's.\r\nFor example for :\r\n        \r\nTherefore,  is minimized when , for . Since we are asked to select the largest minimizer, our program output should be .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 550px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, the base-14 arithmetic function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAAAoCAYAAACCV8YCAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAU6ADAAQAAAABAAAAKAAAAACr2LzFAAAF20lEQVRoBe2Ye4hXRRTHd8u27EmklUul9pJeVvSQlGwzrQgKoohqS7BMCqWCICzpQSjUH63ZP4WxgSH+oYRRRtgTN/CPsswehBpmoWkPoYc9Nev7yTnbcbxz7/3t3p9F3QPfnTPnnDkz98w5M/Pblpaa6gjUEagjUEegjkAdgT5H4HqNXCcc1GcPuw7sVHe5MHxX8X+/N1WfuEO4ucJPHSBfLwpfCcdV4XeMnHwpfJvAFsk/EJYIjwlnCHuaRmnC34RZTZj4QPl8V1gp7FeF/1Y5uU74w2Gj+CnCTUKXsFUw/cPi9xQdqonWC4sF1tkMapfTzUJ3Vc7ZIQsW7YzI8Uj1yQ6zuSLSN6v7nBxvEyopw5xF3i4d30by9Js65MECRZtVzi85m4Xim01cOKzlqWZPJP+UONVIBZJY/SLOIwvmJvFZJbXA2bzVr9nKDX4tzDesnHm/re4K8/U7O1cERwR0XmJZ7zsbbsFm0tFy/rvwYTMniXyfpD7f3xPJG+oOljXPDstMLqOYxkqwXTCbO2KDivvTw1xzSvodJLsJwt3ClW7MUPHThNnCRU6eYqlKvvH4lEGR3M4mnJANh0UDRqvP88kC+Yb4fSKbqrvLwnxFF92jstsQbG19nWExk9T6Vwj6c4Iu1dhRdkvKoEhOWdtC2Jlxwg3CPQIpb7ovxM8U2oRm06eagHmLMmSEbK4R7KXBzc9zituZSiIj/cV5m/p5dL+UzPtQnlFK1yqFpbYFLatdJLv9U04qlrOmXwXWQWCKiCr5QcD+dYEy/0m4WIA4kuybLv1Lkv7DLy1sn06bpDWnh8E22Xj1jxUoh1sFfgGZbq14LoZm0+GagDnJLAJbRJzntkZ+pX0vUFlG3WJMP8SEifbaYPtyQp8r5sC2ib4WHy/+RMn8ednsW5zF2gZ/Q6cEcfTYN3wmfm40ZnXQl3kZkLn4ejvy0dvdq5fbnbnEiSgRHHlao84SJxgnPlXuPC3mCWVKkzU9I2T944JLA+IhXYasnLHleLjTDTpGPAkBLd3Z5P4dGLRURUN0gKyZ3HZ1cmL0JGeDbXzunCDZfIGXAPojhSK6VwbYklUxEURb076xMurz8rB5GcNme+KbzJdPHG/jebNf5IWeJwuyqEPCNqd4xfGe9TbIOZM88X7jwGZjytDZMpqVY/iLdBw5UPxM2yn9++94sfZ9nHNUl6cJoYPPHq9I8IOCfENC3ztZrPc79YmUnDdZdJYTErB3XB/2SYGP2EingDgi5gu8D/PIPqY9z0g6X+JcPp4Isj3U3xT/s1cm+CFBbvPvZmY7Fyt8MF+NlaF/mtobnW6Z+LIZ6Ib1sl3iyCCQRx8H5fl5RtJZMMnkuLLOlMwy2+brlqxDSNHYoFiVMsiSnyyhnSW0/tA2e8pxtbMje48wZUbL0wlfqTPzcuk+EjgTCQK2M4UsukxC9C9kKYOMCw8bMDfIfMM3mZ7AcrSwxkOELKLEdwhUWCoBWwZEI7ltyRBPPGy5wXgGDRdGC/yUaxUgyniKgL4vxCY8IRBQzq8iWiqDTQKZwvpZW0y+sp6Pleq3O9nj4kcKZPp3Tu7ZC9XhexcIBLWQrpbFNsF2LKvdKj1lRtnMEU4VylBeZvI+ne6cFGUmpo8IrG8inQxaKBn6H4WBGXqym6BgQ7aRIHnEUYctQf/HKRXMqVpZj+BLp0wwh2kMWcTxEleXRKXoFFmdJ2QF2zu4QB0CyQb9KygVzHVa3RZhjcNm8Sze5PeJz6KrJMRucpayQhmbzaYdXOSzr7ta5LesnhIfHBkPVZ9zlJ+MK4X1QhY9K2GXMFtYIbwnVE1s5CiBYyB+Q1c9V2l/qczMclCmzG0cycA7kXPvKBNW1HbKD5k/rSJ/lbgh87YLLOzcEh4bCSbueLYsF1YJewtV0Bg54WXxQBXOqvIxQ44+Fwgk4G1KaeYRv0ywfTDPKNK1qc9rxF9kkUlD3RGyLrrhG3JYG9cRqCNQR6COQB2BOgJ1BP5nEfgTlRh1sCvET9IAAAAASUVORK5CYII=\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 183px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eConvert \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003e to base-14, using the letters '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"18\" style=\"width: 43.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003e' for digits \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eReplace the letters '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"18\" style=\"width: 43.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003e' with the arithmetic operation symbols '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFsAAAAmCAYAAACriueGAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAW6ADAAQAAAABAAAAJgAAAADy+E06AAADWklEQVRoBe2ZyWsUQRSHo44LJoILiBsSXIgoLuQi0YMEVMQVBCFGEUTwlJtH/wZF9CAeJTEeNAriAu6oKCiCiOJyijpEBHNQ3DAa/X5ONzRDLzWVmcbprgffdHXVe1X9Xle9qk4aGpy4CLgIuAi4CLgI5DcCjbh+GdryG4L0PN/HUH+gI70h8zvSLVz/AprhTmoYgbn0PQzdYWOMDqt0ddYR2IXlKAgNtnWvzjA0As+pHYAxoa0WleexuQPbLWyzbNKKc9oYD1XTyfdep13V7DQDfR324rIiype852z5vxM2RAXIsF5pQ/08gydRNoWohpzUr8fPXtAJYh68ARtZh9EMOBJnnPeZ7Z+FFYexcYFKaNtNu16YXlxVpZ5z9kEi0QPzvYjoXKxNbdC710UpRYcAzXoTaULpK9w0Ua5Up16DPQdHFVjxEfyNrEjZD9Q2ykMgnftgIntQkv7eJOU8pZEBgnHPC8g0rndhB7yGV9AJZ0D72DDcABNRCvkOfUnK+topl3NUrCmvDNxPoSy7b/AjUF9e1CzxnStv8++XUdCsCnsOXyfp+hSF9iSlQPtyyltBX3stgfrflC+AgnYdPkCSzELhHeglWf3h6RqGWhYjxSQA0hnpOI/pw0ZWYvQC/PGPUZ5aYUcHPPtNJnZhM2o1hktijE94bWe56sVEyUUatHTjRDNjc5yCQZvyr1ajiSxAaT9sgUVQhJ+g51TbZLgNV+AkfII40ZlaPohfcYq2bfW6QRZw2H92zeaHoLOx0lAvNMNb8Gf6acpxspRG6R6NUwq25WmD1Feev5K1Oa4FrYqFoJXcD+2gHCwZX7pE/mpjlPSULrX59WdHV226r2mvzfTeBgq8pBU0O5UCmkDSCHoRE3QTIZqkRXgZ0R5anaeZrQD0wwPQyUOyuHT5F3zlcIk+UHQaiTtpaQXMhopmdQGDPMtVnFee1mrVZmcqSiFaEadMDWz16jmN2PoctJvIzWdQ3q9IbNKIvq7yLPogmgTdaQShhUFWwcw0BvsPx7jEMymf60vaSQ0jMJ2+h6DPZgybNGIzTlZsOnBEh4qKTiFZcT5tPx4x4CCMS3vgvI2nc7iOe8dtHXdpxDxyGz3VVE4h5o+VTU39w6Ezm645r1wEXATqJAJ/Aa2isHQDPrNvAAAAAElFTkSuQmCC\" width=\"45.5\" height=\"19\" style=\"width: 45.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003e', respectively.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eRemove any leading or trailing operation symbols.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eFor consecutive operation symbols between two numeric symbols, retain only the first operation and remove all others.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eEvaluate the resulting expression in base-10.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eReturn the evaluated expression as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003e, rounded-off to the nearest integer.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eFinally, output \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"67.5\" height=\"20\" style=\"width: 67.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"197.5\" height=\"20\" style=\"width: 197.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven a set positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, find the integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"18\" style=\"width: 41.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e is minimized. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIf there are more than one integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e that minimizes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"22\" height=\"20\" style=\"width: 22px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, please output the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003elargest\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e of those \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e's.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"69\" height=\"18\" style=\"width: 69px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-26px\"\u003e\u003cimg 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\" 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src=\"data:image/png;base64,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\" width=\"69\" height=\"20\" style=\"width: 69px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is minimized when \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"67.5\" height=\"20\" style=\"width: 67.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"121.5\" height=\"18\" style=\"width: 121.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Since we are asked to select the largest minimizer, our program output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAkCAYAAAANdf2OAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAWKADAAQAAAABAAAAJAAAAADbokXeAAADh0lEQVRoBe2ZS2xNQRjHWyEpoeotNJE2qIVEbIgETWi8F2iJiIWki7Lx2NqIWCAhIeKxKBbKhiAiQjwiCN2gIlhQ4h0RlXhWovj9kzM309s7Peeee1Vv73zJL/PNnG/mzPzP3O/OPbegwJtXwCvgFfAKeAW8Al6BOAoUxunUA/r0Yg0roQjqI65nOnFToALewG1ohC/gLVBAwq6Ax/AHGiDMRhNwDhSfjISeCHlv+qRWwwOwRQoTuB/x94I+dyhPgEp7jBbqJZDXtoDVn4FVcBaMQGEC7yb2BywH28qoPAQzzlL7Yr77NZYwnQlcTJzy6xKHYMuscXY6YgqUk/LNvkZccDlx2sGnHfHvrfYXlt/O7d2u5iu2Ak1UhMtmBhd+U152BYUJ3JeOVTAZ2mAP2DtgLnVdvwHKbflifVioybtb8XUqSdt20EM5SMKaZG7nml1Wu0TXN24u2DwmadbTEGPCWuf5YIzNMfonuozH6w+lIAE1KfOkNgZthymfwSWIYqcI+pgFZke5mSMmrsD6vpoPd8E8oM/46yBjU6I3g87BbwWlh3RND8KMk0kpkeJaHIG1a5vBNef1rsmE5WDT7zrO4qBykVKpQmW6tp0OOqxnajrsd6V952b6qVwCY2EDzAJjW3COwwfTkG45lQ7m6elIkiv5NtU64+zg5HEKaVgD+o4yuujdRgdTXoli+rmotCDT7tETzWeTqAdhnyXCBMtPuFEFVioxx7Npid7euWBJMMjyE27UHKycOzToNZJSeehpUE+n0CmiMp0Ojli9G7jiuNaVzbe4mX5oaKM+SXXjKAIvomMdHIC1wSAzKOMIPIB+g4MxMil00O8Opi89kwX0pq6DhQk8gh6HQDtYJwAldiV4CXwEtNC9sAlaIMw0xv8+RWj+2bKFwUBNlNeiDCrB1WkcFMFN0Jt78yDu4yvBvwvalOivQjYnzXD/1FYzutYgToLLhnChHo6CTlHJNoyG1/ALqpIvuuq1XDA31xFE57oxVvA26/pbfP0qs69bod3SLWdWZpNonVpfhWOmthbKs8dgEoyCGngJrVANkc1+x6mPfPKJoYy2n6DJfQKlilww/e3zCiSU5m6jtudQB7YVU1EfO1a+4pthP5RCp5bqo62Pw0BQekh13h1Ou2IaQTugJ5vSZCXoAbXBo4BvlN68Al4Br4BXwCvgFfAKeAW8Al4BhwJ/AYL39MwT85uUAAAAAElFTkSuQmCC\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = minB14(N)\r\n    x = min(N);\r\nend","test_suite":"%%\r\nN = [8798950879626654 101528383896576 2 7429908031080];\r\nx_correct =  101528383896576;\r\nassert(isequal(minB14(N),x_correct))\r\n%%\r\nN = 0:20;\r\nx_correct = 13;\r\nassert(isequal(minB14(N),x_correct))\r\n%%\r\nN = 0:200;\r\nx_correct = 195;\r\nassert(isequal(minB14(N),x_correct))\r\n%%\r\nN = 0:3000;\r\nx_correct = 359;\r\nassert(isequal(minB14(N),x_correct))\r\n%%\r\nN = 1:100000:1000000;\r\nx_correct = 300001;\r\nassert(isequal(minB14(N),x_correct))\r\n%%\r\nN = 1:1000000:10000000;\r\nx_correct = 1;\r\nassert(isequal(minB14(N),x_correct))\r\n%%\r\nN = 1:12345:10000000;\r\nx_correct = 9592066;\r\nassert(isequal(minB14(N),x_correct))\r\n%%\r\nN = [1 12 123 1234 12345 123456 12345678 123456789 12345678910 1234567891011 123456789101112];\r\nx_correct = 1234567891011;\r\nassert(isequal(minB14(N),x_correct))\r\n%%\r\nN = 1e6:1e6:5e7;\r\nx = arrayfun(@(n) minB14(1:n),N);\r\ns = [sum(x) floor(std(N)) nnz(x) sum(num2str(x))];\r\ns_correct = [524094678 14577379 length(N) 23971];\r\nassert(isequal(s,s_correct))\r\n%%\r\nfiletext = fileread('minB14.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-17T18:48:42.000Z","updated_at":"2026-03-27T10:30:42.000Z","published_at":"2022-01-17T19:17:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the base-14 arithmetic function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConvert \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to base-14, using the letters '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eABCD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e' for digits \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReplace the letters '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eABCD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e' with the arithmetic operation symbols '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e+ - * /\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e', respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemove any leading or trailing operation symbols.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor consecutive operation symbols between two numeric symbols, retain only the first operation and remove all others.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEvaluate the resulting expression in base-10.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the evaluated expression as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, rounded-off to the nearest integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFinally, output \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(n)=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e contains only \\\"operation symbols\\\", or if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(n) = []\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(n) = Inf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, or if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(n) = NaN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en= 8798950879626654\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(8798950879626654) \\\\rightarrow [B12B56CDD2A75C] \\\\rightarrow [-12-56*//2+75*] \\\\rightarrow [12-56*2+75] \\\\rightarrow [-25]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}( 8798950879626654) =-25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a set positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex \\\\in N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e is minimized. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eIf there are more than one integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that minimizes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, please output the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elargest\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of those \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN=0:20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(0:20)\\\\rightarrow['0'\\\\ '1'\\\\ '2'\\\\ '3'\\\\ '4'\\\\ '5'\\\\ '6'\\\\ '7'\\\\ '8'\\\\  '9'\\\\ 'A'\\\\ 'B'\\\\ 'C'\\\\ 'D'\\\\ '10'\\\\ '11'\\\\ '12'\\\\ '13'\\\\ '14'\\\\ '15'\\\\ '16']\\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\rightarrow\\\\ [0,\\\\ 1,\\\\ 2,\\\\ 3,\\\\ 4,\\\\ 5,\\\\ 6,\\\\ 7,\\\\ 8,\\\\ 9,\\\\ +,\\\\ -,\\\\ *,\\\\ /,\\\\ 10,\\\\ 11,\\\\ 12,\\\\ 13,\\\\ 14,\\\\ 15,\\\\ 16]\\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\rightarrow\\\\ [0,\\\\ 1,\\\\ 2,\\\\ 3,\\\\ 4,\\\\ 5,\\\\ 6,\\\\ 7,\\\\ 8,\\\\ 9,\\\\ 0,\\\\ 0,\\\\ 0,\\\\ 0,\\\\ 10,\\\\ 11,\\\\ 12,\\\\ 13,\\\\ 14,\\\\ 15,\\\\ 16]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(0:20)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is minimized when \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_{14}(x)=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=0,10,11,12,13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Since we are asked to select the largest minimizer, our program output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53930,"title":"Easy Sequences 65: Fractional Part of Square Roots","description":"The fractional part function of a positive real number , denoted as , is defined as: , where , is the 'floor' of . Thus, ,  and .\r\nGiven a  positive integer , create the function , that evaluates the following summation:\r\n         \r\nFor example for :\r\n      \r\nPlease present the function output rounded-off to nearest integer. Therefore, for , the function should return .\r\nHINT:  There are efficient algorithms to calculate fractional part of square root.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 400px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://brilliant.org/wiki/factional-part-function/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003efractional part function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e of a positive real number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, denoted as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24.5\" height=\"19\" style=\"width: 24.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, is defined as: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"86.5\" height=\"19\" style=\"width: 86.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23\" height=\"19\" style=\"width: 23px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, is the 'floor' of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Thus, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"59\" height=\"19\" style=\"width: 59px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven a  positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, create the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"57\" height=\"19\" style=\"width: 57px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, that evaluates the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"139\" height=\"46\" style=\"width: 139px; height: 46px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAkCAYAAAANdf2OAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAWKADAAQAAAABAAAAJAAAAADbokXeAAADzklEQVRoBe2YbWjNURzHr8ck85CnMMZSJhQtLG6NPJU3LGS1d8gLpSgtLa/kHVrykJgkaeKVpyykJZI8tEhebGpmM7QwmYe14fvd/R2dezpn/3Nbavfe86vPPef8ft/zv+f87vmf//nfWCxYyEDIQMhAyEDIQMhAyEDIQOoZmJlil4HQ54M4yEmxb1bJ52C2l8H3FGZdBm0DeA1OSlmLsgQEkwwUoKwG3eAP+Al8bAtEv8ExMEA6cDWfBl2gVHxZXazH7MvBOtACfBO8CVr+II1gBNBtJBpNgEleqweyvc5V7JNgrtK3ot3rSFqFxJ/Y4rxANlqH56RXQZcr2nuOPspfiPgihybr3FWYsc8Kvig6PgyHOrJE/w/RnTM1Pit4PDqNNTpyL8o3fJnYXCmTakDZ6Zgg/fUSi5saW4K5zPeDa4D7z0cwBdB49jsLPgMeV2pBptowTEwtrC8Rk2yXOLcTdcrocQ22dGyF7wHYCiaDRvAcTAA3wBVwCuwAxWAeeAF8bANEy32EEZp9iEdNOuISkeFJmkIlUHMlVVWc28VE8D4p6mjUwM996ggYDriiZwPaYsAY4a/ma5UQqn59KVP5TtvYqmQcvZ2D49pYz9suovkuaNqFmj9mW8GMDwFLRXgV5QlwALwS3ywp21A2S92nuASRuoaP3qXhFvW/jS8WyrpUxVH+0vzcWv6ZK8FLoOCDjLch999n4BFQViSVO8rhWT6EjqSD6bf5qIgB6/FWXetK8GoR1aFcA8r0TqivkPYtw59JzQ/aZEZrdVt1jOZMSrDmT6ryrYR7JG/FvKRIoq32T3W6MCT9vumzB3MSvIM5V97BvRnj1H01RbYVPA6iBSI8g/KN0YlvN7SXoKWn5v+RTqcIzuomKAXTAI9fTKJp9E8V510zaGvzgrwQN3le2DQ+qBg/bAY82pXSl/37Qq7Hd/Um8V3BJdo4+RenzebCqeay0RTYVrDaf+9D3GR04IuJuf/Oh68edBhaWzOdThEcfw34BvjALwa8a01bJo52lNfNoK3dDCd/kZ2WIJPJWCfg2XgG4BnR9kYId7+1aoyM89CPV67BbhftY5SDDBEX6FOJ7zJi1iZvA34xmQ5M2wwHY58AVzp/Ye7Z6WQ5GKxaRJxLgcfgD0FDbbmhrRC/93a5Wzrw1dhmPDVw9fLLqMkD6WJFGOhxwAczx6/gseoo2AZcxjuUSeR2cRvsAXwHYPsg4IPOas6AVZ1w8j8JPjXrQHfClTWfvFsLARfaO8DjbBsIFjIQMhAyEDIQMhAyEDIQMhAyEDKgZeAv/Qvne8Rn4VIAAAAASUVORK5CYII=\" 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0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-39px\"\u003e\u003cimg 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\" width=\"725\" height=\"89\" style=\"width: 725px; height: 89px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the function output rounded-off to nearest integer. Therefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, the function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e3\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eHINT:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e  There are efficient algorithms to \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://math.stackexchange.com/questions/1277652/calculate-fractional-part-of-square-root-without-taking-square-root\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ecalculate fractional part of square root\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = FPSR(n)\r\n    y = sum(n);\r\nend","test_suite":"%%\r\nn = 1e1;\r\ny_correct = 3\r\nassert(isequal(FPSR(n),y_correct))\r\n%%\r\nn = 2e2;\r\ny_correct = 93;\r\nassert(isequal(FPSR(n),y_correct))\r\n%%\r\nn = 4e4;\r\ny_correct = 19933;\r\nassert(isequal(FPSR(n),y_correct))\r\n%%\r\nn = 6e6;\r\ny_correct = 2998572;\r\nassert(isequal(FPSR(n),y_correct))\r\n%%\r\nn = 8e8;\r\ny_correct = 399984981;\r\nassert(isequal(FPSR(n),y_correct))\r\n%%\r\nns = 10.^(5:10);\r\ns = sum(arrayfun(@(n) FPSR(n),ns))\r\ns_correct = 5555495122;\r\nassert(isequal(s,s_correct))\r\n%%\r\nns = 1:1e6;\r\nys = arrayfun(@(n) FPSR(n),ns);\r\nss = round([sum(ys) nnz(ys) mean(ys) median(ys) mode(ys) std(ys) sum(num2str(ys))]);\r\nss_correct = [249667208414 999998 249667 249697 482817 144222 372905871];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('FPSR.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-19T05:39:40.000Z","updated_at":"2026-03-28T11:35:31.000Z","published_at":"2022-01-19T12:00:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://brilliant.org/wiki/factional-part-function/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efractional part function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of a positive real number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, denoted as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{r\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined as: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{r\\\\}=r-\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the 'floor' of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Thus, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{ \\\\sqrt 2 \\\\}=0.41421...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{ \\\\pi \\\\}=0.14159...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{10\\\\}=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a  positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, create the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSR(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that evaluates the following summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSR(n) = \\\\sum_{r=1}^n \\\\{ \\\\sqrt r \\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSR(10) = \\\\sum_{r=1}^{10} \\\\{ \\\\sqrt r \\\\} = \\\\{ \\\\sqrt 1 \\\\}+\\\\{ \\\\sqrt 2 \\\\}+\\\\{ \\\\sqrt 3 \\\\}+\\\\{ \\\\sqrt 4 \\\\}+\\\\{ \\\\sqrt 5 \\\\}+\\\\{ \\\\sqrt 6 \\\\}+\\\\{ \\\\sqrt 7 \\\\}+\\\\{ \\\\sqrt 8 \\\\}+\\\\{ \\\\sqrt 9 \\\\}+\\\\{ \\\\sqrt {10} \\\\}\\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\u0026gt;\\\\\u0026gt;\\\\\u0026gt;  = 0+0.41421...+0.73205...+0+0.23606...+0.44948...+0.64575...+0.82842...+0+0.16227...\\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\u0026gt;\\\\\u0026gt;\\\\\u0026gt; = 3.46827...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the function output rounded-off to nearest integer. Therefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHINT:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  There are efficient algorithms to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://math.stackexchange.com/questions/1277652/calculate-fractional-part-of-square-root-without-taking-square-root\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ecalculate fractional part of square root\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58284,"title":"Easy Sequences 117: Fractional Part of Cube Roots","description":"The fractional part function of a positive real number , denoted as , is defined as: , where , is the floor of . Thus, ,  and .\r\nGiven a  positive integer , create the function , that evaluates the following summation:\r\n        \r\nFor example for :    \r\nPlease present the function output rounded-off to nearest 3 decimal places Therefore, for , the function should return .\r\n---------------\r\nNOTE: This is a follow-up problem to: Problem 53930. Easy Sequences 65: Fractional Part of Square Roots.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 392px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 196px; transform-origin: 407px 196px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 48px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 24px; text-align: left; transform-origin: 384px 24px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://brilliant.org/wiki/factional-part-function/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003efractional part function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof a positive real number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.5px 8px; transform-origin: 41.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, denoted as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 24.5px; height: 18.5px;\" width=\"24.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48px 8px; transform-origin: 48px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is defined as: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 86.5px; height: 18.5px;\" width=\"86.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC4AAAAlCAYAAAA9ftv0AAABmklEQVRYR2NkGKKAcYi6m2FYO9wLGCs3gPgenWJHH2rPRXz2ERPiO4AG7APiLjo5fBrQngeE7BuMDicqoEYdTsVkNBriRIXAaIgzMBAVUKOZczglFfQaUAnoOSkgvg7Eb/F4lO5JxQbomBogFgZiE6jDvIH0NiBuBeIqqNhOIO0xmBwOcwuyI0WAgs1A7AbEylAFZ4C06WB2OMiBc4A4BerQCCCdAMQtQHxkMDr8NDSpTAfSIMeqEkjT6H6gexoHOQCUvt9AXXIXSHcD8Uw8oYtNakAcDgrh5VDXvAfSQiQ6GqR8QBwOaktnQh2bQUZoD5jD3wFtFgRickN7QBwOqnAuQEO7DUhXk5FMBsThZUBbO6GONQDSePuMeDxF9zQOKwZBpYkKmaFN9xBHLgYpSSZ0dzisnQKyuJyCZEJ3h1OQMjC00j2NU8vxow4nKgSoFdwDVeVTw/1EBRSxnWVQuXwHi6sWAMVWkOlaUIXlhEWvGVCsA4jxjlUS43DQaK0ODseBumHk1pAUmUuMw8kMUNpqG3U4bcMX03QA5iahJnPpayQAAAAASUVORK5CYII=\" style=\"width: 23px; height: 18.5px;\" width=\"23\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.15px 8px; transform-origin: 21.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/floor.html#\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003efloor\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Thus, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 116.5px; height: 27px;\" width=\"116.5\" height=\"27\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 105.5px; height: 18.5px;\" width=\"105.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89px 8px; transform-origin: 89px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a  positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73px 8px; transform-origin: 73px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, create the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.5px 8px; transform-origin: 143.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, that evaluates the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 143px; height: 45px;\" width=\"143\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 140px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 70px; text-align: left; transform-origin: 384px 70px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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\" style=\"width: 764.5px; height: 119px;\" width=\"764.5\" height=\"119\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 284px 8px; transform-origin: 284px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease present the function output rounded-off to nearest 3 decimal places Therefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66px 8px; transform-origin: 66px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 37px; height: 18px;\" width=\"37\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.5px 8px; transform-origin: 37.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e---------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98px 8px; transform-origin: 98px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e This is a follow-up problem to: \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53930-easy-sequences-65-fractional-part-of-square-roots\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem 53930. Easy Sequences 65: Fractional Part of Square Roots\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = FPCR(n)\r\n    s = round(sum(arrayfun(@(i) nthroot(i,3)-floor(nthroot(i,3)),1:n)));\r\nend","test_suite":"format longg\r\n%%\r\nn = 10:10:100;\r\ns_correct = [3.964 8.800 14.192 17.034 22.718 30.851 34.152 36.411 40.460 46.164];\r\nassert(isequal(arrayfun(@FPCR,n),s_correct))\r\n%%\r\nn = 1000:1000:10000;\r\ns_correct = [519.723 976.838 1468.549 2014.691 2524.371 3002.235 3519.174 4089.723 4495.781 4933.097];\r\nassert(isequal(arrayfun(@FPCR,n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 49729.556;\r\nassert(isequal(FPCR(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 502449.723;\r\nassert(isequal(FPCR(n),s_correct))\r\n%%\r\nn = 10000000;\r\ns_correct = 4994309.968;\r\nassert(isequal(FPCR(n),s_correct))\r\n%%\r\nn = 123456789;\r\ns_correct = 61767172.780;\r\nassert(isequal(FPCR(n),s_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-05-10T11:29:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-05-10T11:29:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-09T11:57:12.000Z","updated_at":"2026-03-28T12:56:07.000Z","published_at":"2023-05-10T11:29:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://brilliant.org/wiki/factional-part-function/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efractional part function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof a positive real number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, denoted as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{r\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined as: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{r\\\\}=r-\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/floor.html#\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Thus, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{ \\\\sqrt[3] 2 \\\\}=0.2599...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{ \\\\pi \\\\}=0.14159...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{10\\\\}=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a  positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, create the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{FPCR}(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that evaluates the following summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{FPCR}(n) = \\\\sum_{r=1}^n \\\\{ \\\\sqrt[3] r \\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{FPCR}(10) = \\\\sum_{r=1}^{10} \\\\{ \\\\sqrt[3] r \\\\} = \\\\{ \\\\sqrt[3] 1 \\\\}+\\\\{ \\\\sqrt[3] 2 \\\\}+\\\\{ \\\\sqrt[3] 3 \\\\}+\\\\{ \\\\sqrt[3] 4 \\\\}+\\\\{ \\\\sqrt[3] 5 \\\\}+\\\\{ \\\\sqrt[3] 6 \\\\}+\\\\{ \\\\sqrt[3] 7 \\\\}+\\\\{ \\\\sqrt[3] 8 \\\\}+\\\\{ \\\\sqrt[3] 9 \\\\}+\\\\{ \\\\sqrt [3]{10} \\\\}\\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\u0026gt;\\\\\u0026gt;\\\\\u0026gt;  = 0 + 0.2599... + 0.4422... + 0.5874... + 0.7100... + 0.8171... + 0.9129... + 0 + 0.0801... + 0.1544...\\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\u0026gt;\\\\\u0026gt;\\\\\u0026gt; = 3.9641...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the function output rounded-off to nearest 3 decimal places Therefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3.964\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e---------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This is a follow-up problem to: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53930-easy-sequences-65-fractional-part-of-square-roots\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 53930. Easy Sequences 65: Fractional Part of Square Roots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53940,"title":"Easy Sequences 66: Fractional Part of Sum of Consecutive Powers over a Prime","description":"Given three postive integers, ,  and , create the function , defined as follows:\r\n            \r\nWhere  is the th prime and the symbol  is the  fractional part function of a positive real number, defined as follows: \r\n        If  then , where , is the 'floor' of .\r\nFor example for ,  and , we have:\r\n        \r\nTherefore, since :\r\n        \r\nPlease round-off the output to four decimal places, so in this case: .\r\nHINT: This is related to the Faulhaber's formula.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 355px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 177.5px; transform-origin: 407px 177.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106px 8px; transform-origin: 106px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven three postive integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ee\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73px 8px; transform-origin: 73px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, create the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 85px; height: 18.5px;\" width=\"85\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62px 8px; transform-origin: 62px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 181px; height: 45px;\" width=\"181\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.5px 8px; transform-origin: 77.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth prime and the symbol \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18.5px;\" width=\"18\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the  \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://brilliant.org/wiki/factional-part-function/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003efractional part function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.5px 8px; transform-origin: 143.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a positive real number, defined as follows: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 46px; height: 19px;\" width=\"46\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 86.5px; height: 18.5px;\" width=\"86.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 23px; height: 18.5px;\" width=\"23\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is the 'floor' of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36px; height: 18px;\" width=\"36\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" style=\"width: 49px; height: 20px;\" width=\"49\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; 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\" style=\"width: 430.5px; height: 35px;\" width=\"430.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 210.5px 8px; transform-origin: 210.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease round-off the output to four decimal places, so in this case: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATAAAAAlCAYAAADFl7VvAAANaUlEQVR4Xu2dWcs1RxHHkw+g0eiViASjoCgoLlHcQMEdRIi4I4LBFYSgxrgh4hbXOzUKQhD3BUQ0qAEFN9xRULxwwQvxyt0PoPWT8w/1lD1d1TNzzvs8oQeK5z3n9FRXV1f9u7qrZt7LL5vX1MDUwNTABdXA5RdU7in21MDUwNTAZRPAphFMDUwNXFgNTAC7sFM3BZ8amBqYALaPDdzN2DzL6KP7sJtcFjTwGPv+30a/nBqaGkADE8C22wHg9Smj10/H2q7MhAO6/pDRl40+e/TeZgfnXgMZgN3bRnCPlaPwKyWGd/8Cn99Ym78W2qlJ5Ps9dy+rdeT3IPvuTgn/kRWe/r9udN0geCHHaBQh2UfkG1DlmaZeT16na/mN3Pc0a/xAo4cY/d7o80FX0vkH7kAghq1y/dnoDyPKGmjLnD7Z6KrDPV+1v7cW7gcD/mlU9cuejz3f+Lx/YIzy70VcqADY/azDFxk9Jwz2G+EznT3MfUdE8t7DZ357otFrQht+Fh+Uy/VTI4zzto7SmPA3Hybk7/b3x4d772N/P2f00MNvcXwo99lGbwyy4yi/M+L+q43gyQrPlrAHNIDXt4w0zsD2/z5K7mvslyuzxvY7enuJ0Y1GHzHCkJ5wkPPV9rdigIVubm9yw6Gvu4ab3mWfP2hUNeKRPmmLk7zW6LlGfzN6n9EXO/2hlx8ZXZvMz6gcp2zvx3zToeOX2l/scK9oXvYDX+wavui1ApKS7xXW/sFFPdPfb42i/Uiv+PpTBpT8E2sLpiz2nwGY+sLxvus6XmKoEB+we7pRdLDI57HWRis8CgN8BII47FsaRoyRf+Ygy8vtrz93AqC+fVBgT1kAjwAztnuZ/XbzgT9A9gwno9c9zo5hAHrZhVzvcX3CNwMwRRroI+oScEXHAMubss6Lv8tYlpqjpxc05qPIfrEZ8/nhw5yNACXzROT78K0CXIL7ZaeAtQdhATNg0/KfEVHp40tG8GLuXmlUAS5keLsRwKWrCmD4BHa+dHl/z8bieW0GsOjUPecTSN29YexsD752kLzlxIAY0ZCuOIke4QE7jD9eAriec3tnjSAIPxxKE9hyXMmBUWRnMejuCqNfGX3SiNWpAmACqdY4vR62GjrjlbGgC0U+zAWJCaI/rah7AmbU8/MKuoxzTbTyMaNqBNwwl5N/5UGqZXt+kW/5UEVgv8iPLAravmOrbzNSMFEBMNnkG+y+rcmsasBUPsT3Dk1khOMuXXR+i1ErMnmnfa/t2xIAeXCJDuMBcMmZUORfjJYcW79L/tbk+H5oFw1pJPryelLklwGYn8ClcWhOAPxHGK3d3kkfSwDiZcnkrjiX2vgVdi0wasubRbMjch27rcaNLgGIVlQEMBM5LflIT0Y/X1ui5lIE5ARhoX53Z0xVvQoIv2k36NhqcwRGqKtVOFspdd7VikyyyIdB+u1dnECv1B6Q/udgAC3jyKJAZMhWAPRB/6PbtyqAKfrqGblfZbdEYRje441a0ayMzs9bZTXOjNXrlzPPtdtAReyZTWbynPJ3+VJv3D5gGInCfGTes53KeEcBDNClz+uNRpNxXh5s/y5G7zDSsdUmAGMv/QvXAytDBAba/MmoFwVUIp8IYHFl9k7bmyCUv7StqESBEcC8EQkA14BGBcC8noiuls7Y/LxkUXHPYNHVD4x62cZRY84cRBEG7dbo0fOHF2DQA+BMnlP97hfP3pz5I5sRcPbAtzaqlS5G5tz7pe6vJOOi3hn364yeZET1wy4A5pXZWjWE+kvhsIT0g+w5Zi/ai1kO5CGrMbJ98s6zZBx+zFFWAeDIyigdVADMg2e2hSDS5Orpcw/n9Nue+w7qO/bvndjLrVKC0dWbFRuDvwjbSA8KrfMv6crbQHVxigGCAg2VNYyWaIwAmPepON+9RJhvq8SGkmZeB5siMG1n6KyF6qA+oXyWHq2co/WAQ4P1bfhuKVvZctyYJGhFk/6QFR4R5ARC1Qyul6MCYH58VQCjjzWAWgU3zV0mT4Wftyf4sWD5jBc8WJjYilRq0ORorbnM5KnUBWY8+L0iJ+382KsAVt1iR98hueETMPTPgkGJSuWQfQTA4A3g3Nno0UacXTEf/soibY4pOPfSscxuAKZVHmFQ+q+N7ml0LyNqkihH6E2GBpGdoyHwV4x01tY7a/FgCH8c4VVGWSSWAWRMIbcclnFQd5YBdpi//32sAJg3nAww/NzscTbVkpnvtMKOpMGXeHk7oA21SWxhuR5l5J0uM3rukb7WyObPW5fkzb4fSWz4/qoAVuXvwRGZWdgpVv2XEf7KmZJApbK9HAWwqCdfHsNvjGMpemdXQxTtd1O7AFg8C/LFq9dYhwKbbPWL52hENZyZcaHcxxlpFWbFqVS2RxCrRGJ+khkLk6oL51HBH9/5Qlw/OYDGaEGe7h8FsGxh8A5xLACTDWRgGg249blyDupr+eCRRZaSb+SsSLLhOBQ9b7n+YTdXz99G5kuLUxXAsgSZrytkvNnisBXA6CP22fIpBS4kknzR+C4A5g+8W06L0riyLFKsIyNUJNOgi6QAwv8wDCIzrAhiS6AjPn71j08S0IaqempgqPJeiuZOCWDZePbODrb0jdORSGCFrBRC9uasmn30dpfpQDyzdpktneJ3D2C9iNEDfRXAPOAtnUf788dsEd4DwNApxzYEJQQ7sc9e7dguAOYdpGUgRDQ/N8oKCf3EVcLXEWOK24ClSKSXWRzp75QAlkU9x95CqrYnro4j+vJtqwmKWMvU265fVADbewtZjdh8u15CZi8AY/4VaEQwVqlVK4LdDGCVcB/wqDy35R1tzVlFz2HiofsSQPoJyVafXn/HBrCqkyNj1WjXAI62/dlWY4S3P0qognMWgWwpaxmRfY+2a7KQmZ4kl3YXmb6q29g9AUxz5GXT4vhCGwDndPF6gH1x8+FLf+R0Jkvdy6TFmqtWmprwMNtWxKr2tdm73nN4vo+lrE0WTVYNlANt6FiH+D5TmhmvAKyaqaqOUedQGNet1ZuK7SRztohUwXnLIf6ps5Dep6oRWHXH4s9Xe5HVpQAwLcq+bGZtAuXMDqsHJv58KXOknu1WCkezCItHg7LD3J4zV6LJov/dnklcC8RkbbNVUlm/XjsfqVWNvDLGY4IX/WshyXRQBToBWGYfrbGvdSLPKxuHb1tdnHz0U42AvZ/1EjpVoDtGBOZr2rIECj6rZzFZoHUmfeah9J4T+uK0NRkeTZznk2XVWkYmR82ybDL4VuFfJZqsODdtttQdVbKQvg/+vZTh9YmRTDfVsenAtRd5YVi8261a+xT79nIvjc07egbOSjJU3goSZcmcqKK3kSwk/GQDveJjZctHnnP12/Oev8ofs6h9TwBTMFQFY/S06QysUvBZmdzIZ42jCXx6huy3kC0l7RVNMuYtZ0NVAPNPHCxl1xTJtKJjdEadHhnV6hZQKe8v2D29pAy6/I6RDmD11greVcY73LIjBR8NL82pn8+sRIezH2TpvWCgYqunauMds3Ue7PWz9LYKSn5a7/WSTSyBk+edBSVVANOCtlTpLwzIjgyi/jcBWFbwWZ1sH/msfdzFK3JpwgEGws2lre5e0aTGDT9KQUadpgpg9CMnbq3C/kwhljd4ncOnEvUKvACLmzqTS+Ey9X/+jMXrthox+DltAZT0lJVGSA97J4aq9r22nbZ7LXuVbloO7wOCVmGod/oWQPV4x7FUAcyXJjFfHzfSdk92Be9KbaeXYTWAxazemucNESTywbjX1BL5kBtjZ4v46cNIyVTw8Gfv1SPx0aPMKSpGyeTeGBw5uy+WcVScTmDkX0gHH55YiC/DU/9xvNnCEYsNs3HEqClW1mcru/jLif2zcv5JiMo8EQ1iU2u2j9k4j/27dgX+fV2au6XX4Pht4tLLDLAZeFN3xVzozcbiXXlqBaBkgVblfm8u4jki9sZjTFcYUZxOdNx6MWmm31UAxuCfaeSLTOmIfX6l3ktC9fiM/ocMTIYUwAQ+0oi6JMlI8WkrnGYSeB1zq9L6Z/Y9K0W23VlSsrZ4lRcaMhG8Cxx54oUc3zfqbfO0RSP64UJmtnBLr9wWCHCfHLvn4ICxeC+N138fy2aIFHm9NRcJiiqA0T6OTXZWee2x5uAYmdKKHvZog2081Ug2WrEH9M0r3j/RsRt0w8soo59kbx3p+YyKzVvPUUZ/p+0fjSrzuKRHfF1vd118m+yaTNoeE3dH4IEh8YbVrW9nOKYuAKerjEa3umtl6r2HbS3Ppft0AL+mnGVvWSa/S6SBCWDbFE90yHUqgBiRVlv4a+2m0f8BaaQfta28GHEN39Y92kaf58Vjr7FOPh0NTADbbh6cAdxipKzcdo7bOehc663GqpqF3NIrW4gXGx3jP/2Icp0amLfoZd57ZA1MANtHwbG0YB+u67mwdczOO9ZzP3snZxWcffns0168W+A1/xPhY2n3AvKdALbfpHEmdopoZz+JLx4nto6jb2y9eKOcEpc1MAGsrKrZcGpgauC8aWAC2HmbkSnP1MDUQFkDE8DKqpoNpwamBs6bBiaAnbcZmfJMDUwNlDUwAaysqtlwamBq4Lxp4L/w/QBiMZ7yYwAAAABJRU5ErkJggg==\" style=\"width: 152px; height: 18.5px;\" width=\"152\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHINT:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.5px 8px; transform-origin: 68.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e This is related to the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Faulhaber%27s_formula\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFaulhaber's formula\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = FPSP(x,e,n)\r\n    y = FPSP(x,e,n);\r\nend","test_suite":"%%\r\nx = 10; e = 2; n = 6;\r\ny_correct = 0.6154;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 100; e = 3; n = 50;\r\ny_correct = 0.6288;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 100; e = 4; n = 100;\r\ny_correct = 0.2495;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 250; e = 5; n = 200;\r\ny_correct = 0.1415;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 123; e = 6; n = 200;\r\ny_correct = 0.1292;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 10; e = 10; n = 300;\r\ny_correct = 0.7006;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 1234; e = 56; n = 789;\r\ny_correct = 0.8419;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 3000; e = 300; n = 3000;\r\ny_correct = 0.6441;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nxs = 20:2:2000;\r\nys = arrayfun(@(x) FPSP(x,x/2,x),xs);\r\nss = round([sum(ys) nnz(ys) mean(ys) mode(ys) median(ys) std(ys)],4); \r\nss_correct = [472.0982 numel(xs) 0.4764 0.2518 0.4704 0.2854];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('FPSP.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2022-01-20T12:19:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-19T18:18:26.000Z","updated_at":"2026-03-28T13:08:19.000Z","published_at":"2022-01-20T10:08:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven three postive integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, create the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(x,y,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(x,e,n)=\\\\left\\\\{ \\\\frac{1}{p_{n}} \\\\cdot \\\\sum^{x}_{i=1} i^{e}\\\\right\\\\}  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth prime and the symbol \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://brilliant.org/wiki/factional-part-function/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efractional part function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of a positive real number, defined as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er \\\\in \\\\mathbb{R}^{+}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{r\\\\}=r-\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the 'floor' of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sum^{10}_{i=1} i^{2} = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_6=13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(10,2,6)=\\\\left\\\\{ \\\\frac{385}{13} \\\\right\\\\}  = \\\\{29.615384561538...\\\\}=0.61538461538...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease round-off the output to four decimal places, so in this case: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(10,2,6)=0.6154\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHINT:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This is related to the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Faulhaber%27s_formula\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFaulhaber's formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55345,"title":"Easy Sequences 68: Factorial Rectangles","description":"I'll celebrate my comeback to Cody with this one easy problem...\r\n----------------\r\nThe rectangle below is special:\r\n                                                \r\nIts area is  which equal to . We call such rectangle a factorial rectangle, which is an integer-sided rectangle with an area equal to a factorial number. \r\nIn this problem, we want to know how many are these factorial rectangles.\r\nFor a given integer , we define the function  as the number of factorial rectangles with area  The factorial rectangles with area  are as follows: , with rotations not allowed. Hence, \r\nWrite a function that will calculate , defined as follows:\r\n                                                \r\nFor , we are given:\r\n                  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 556px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 278px; transform-origin: 407px 278px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 200.5px 8px; transform-origin: 200.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eI'll celebrate my comeback to Cody with this one easy problem...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e----------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97px 8px; transform-origin: 97px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe rectangle below is special:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 142px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 71px; text-align: left; transform-origin: 384px 71px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96px 8px; transform-origin: 96px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: middle;width: 182px;height: 142px\" 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src=\"data:image/png;base64,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\" style=\"width: 47px; height: 18px;\" width=\"47\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49px 8px; transform-origin: 49px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e which equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15.5px; height: 18px;\" width=\"15.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. We call such rectangle a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efactorial rectangle\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.5px 8px; transform-origin: 115.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is an integer-sided rectangle with an area equal to a factorial number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.5px 8px; transform-origin: 230.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, we want to know how many are these factorial rectangles.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62px 8px; transform-origin: 62px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75px 8px; transform-origin: 75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we define the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFkAAAAoCAYAAACVdVbLAAAFd0lEQVRoQ+2ay+unUxzHv/MHMLmsNEkuCyvCsEGxQJSmkFvJCiNZINcsJGZIKWlQlJQQNmqmGWos2BiXyMLCpdnYuSzmDxjvV51PfTpzLp/n+3u+J/Q89e75/Z7LOZ/z/lzP5/luWy3HxhnYtvEZlglWC8kDjGAheSF5Fgau1yi/Cz/MMtpqda/GeWPKWP93S75NZFwp3D+FlM6zKO1B4U7hz8i4WyX5bE1yhpvoWGYxl+v/n6LCRASe8AwE7xI4z30w5sPCdZG1rUMyxN2RhD9F51+FX9IqrtX5b+GIcFq6tnPuFQbGQ8ZPhPMiJATGKz3yqC6eJXS9ZArJF2jAFwSI5HhM+Ej4zUmAZX8gXJKuvRYRYs1F1l5DuT+ned+feWw/HPN8JRA6DrTmiZKMe+wTzHJv0t+1RGKTn5MU8eIGF1oaGgu7Rzh3wLzGS9NjIiQz0HtJYELDZUIv4JOBXxdu6Gl5ZiJGWbGJbfM9oQvViqNHMrHtC0cE1unDQ40jQsv3wukBhczJsyl35Lx4+DUtz2mRbFoiRHDc19JWganJ9eQMbH+dxhiZbM3TL9TcxRDaIhkN7U5CUzGcOgMJmxwCo/hDeF54auJEeOyX7h3GOl/IS9LSsOa1VSOskWwC26BUEqMT2ESeVhbaerJCChXSRQJVECGQigiLZN0PCU+6yW/X370q5bieqVZSNZItttlcVVeYysQGnzeZr8isMp/SrPQB3bg13YTIz4SDAsn9HWF/uveNzr3wA8mHBDYnJxw1ktGcCfBfCBUsjNKNOr5HspHwnLNYeCCevylYlQBxHJFaH+VQMhbLxhrJf+kFS3gRTZYUOPraVJIhlXBBqMB6Wa/t3izOsoZIGQrJhKAinzWSTYtMYvFqNGlT55tCss85uHluhX5v0CtzkXPLJK+TracSNMfzU0j2JDJ3Xv9buKzG2UzgZuk4MlzQInwmuajFuqNJWDI9BT0ua0mWRLYnXSMvEBsvFrBCFvW04HeeRlwkJvvytGREFi6je4MtJz5icqilFzBHSzalOE8J9rbgt+3mhj5kWRWRJ+RoCYeYRmIpqft4HK2qILnq8TVLzt0pOhkCfi7UGiaWbEoCYaHvJoWavowMX6v6eJrXsM16NQ3qSSzJYWGHZBhpMplyq/V0K6gbIebauXvmhms93Kt0o7S99OT4jE17tNQPMeGxNqoAe8aTlIcGYinxtVXXGonIXzIeW7eVbngOR60BZJ5V7ev0ehf0S3mZA62/VSAEkh4RsP4awbxv3oGFEH+NNEICu7RcMUZGHlp8Uso/AdkcrUaWhaCSpbIWrnNgCCcLfAFpKY3xOIobEW70yhOs71nB9zA+1f/fCdsFEhH1IVrvWbolGxZxd1rAXTrXLM/Xsa/quR3pPZvvJf2fe4A1tfbqXqkN4L2pFCq8l6BcEnGrtWtKaW69eyQnJa0Y7FLhTOHqdPFbnX8U2I72+su8wicqCEUhR9MYj+tcIsSTgZXThLd3S+SanJxbTXv7usNzJe/hOskZ4zks4LmttTHXLUJz2x0l2S9inb9rGbsWKnxowZJuFvgIEE1GeMGHwiabWhge1n6j4Dt4J/AzimRLDvmXFaym1Ja00OK7Y7QxOSJ1MEr9WGh9JlvHWPw7GAjW3lXkKJIt2USaLSzEQovfDFjCi27zqU5eFuaq8T3B4S/VvDSKZOuFRJotPrT4KoEdo7Ufo3JbDA7/ECVg3pN/MBMVNjB39RFPTuQbYWszULLwnmzEzpOEuX6mxXqaPwHIBdo0yQj0imC1Nq7OV4fax1jfr0DW/CuH7wFHvlj0FDDk/qZJHrKIf/skC8kDNLSQvJA8gIEBUyyWvJA8gIEBUyyWPIDkfwDbBkY4Wm/IcwAAAABJRU5ErkJggg==\" style=\"width: 44.5px; height: 20px;\" width=\"44.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150px 8px; transform-origin: 150px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as the number of factorial rectangles with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 19.5px; height: 18px;\" width=\"19.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5px 8px; transform-origin: 43.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The factorial rectangles with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAAkCAYAAAC+PdWUAAAEuklEQVRoQ+1aOasUQRB+7wd4/wOPwEgDj8ADFDxQEAPBM1Pwiky8jcTroQaCJxirKBgpiqCgYqKIYmDggZGR1z/Q74MpqO3t6mN239uZtQcK3/ZUd1fVV1VdXePoSHlab4HR1mtQFBgpIA6BExQQC4hDYIEhUKFE4n8C4jzoOcnQdRvGz4O+et7PwNhc0EfQz5bbirpMMfS0VNN2e5mpv9iO06L2i0UiF/sEmmYI8Rjja413rzG+ABTiydRtwtmp/07QYdAR0PUECQ5W/K7NTmP8YsShl+L9cRD3vVs5zl78exV003KiGIgU6FxA8GV45/MyeuE7NW+WJUCCUQbF4oKxJwFEcVxLZjr0dgPILRi/VTm95hFb/sY7BkVX1guBKFGY6oFacHrUCzUwH3+/HxQamfvOBD+j7wNoOYiRwCcGojg8+e5VQHGtTSBGskQmI/KYI5N2ep+tZO03mLfQ1ScE4m4wn7HQjxiGDvCj4jE9KNO4g2DXzhgCUfTdCiFvewTV69Ae0x2eR/i9BuQFCeN0hi+WM4VA/IxJ3PAAKHq4egT/q0B0hR4EIHX2TAWRDr8CxJRoPTrV6mjTUeiLUlmPePBY6gLaAlHysxaIky+AnoBSqk1z0zrWHNCcVBCZ7l6BQlWori80iKcw72ilnxXJfM0I31zxddQYFogCgM92jM4NEYE5T1LEnYiHDgifpG1TQUxZTECk/eaoQBA7cY1Q7aCdoAPsUDqlApNBSyoPIPr6WY8fDwPSi+eEUoQ1Xd+TUgxk8XzHC98dNnXNfoJ4BZuySHKd+hfGpOhJBbHDprErhlaWKZaCyIauR7mG0dVayv1Kz3er21Sju3yxijK2bj9BlOzmXsukdsiJxA5HyAGRmzBCGP68r/A5BBozLMHD/hoolOctI/KwD91PY8aX95fwRyhbxNbpF4iyju9oSS0AtSw9gUilWe6yyGFEhroxsmmb7oguqP0CkY4/G7Qa5KZ3DaI+K11Z1mHgQTXYM4hcR/K7784jm4sB2titcXXg77qpWe7bvIL4Gh4Tnk5FOfGKEIjk5aHd1jsi5e81EuUOGCoC61SnHQ6Veya6HsouAtOE9fAwD7235g1DdUoAn4F2gELnsmQ12iK1Ou1wirogSiSyu74vACIVqdMzbXt1mgogTacbK6GULRHb1casC6J4T+yuGMA3+KrN1akUfqEIlEzDDo/+3BcKCrlPdlW4PhBlA+uiLM3Y2HdC8q0CsU3Xy4W7riP0Y17umShXMH4LtK5elItB8BwkzXKrmyM66Mq0K+X6QNQdBN4D+TFSeqUiJBffFUiV2rt4bi5Wa/TDuBO1Rg6IYhtW42cDAq7Eu0Ug9zohDXJfSpVU6r2X+0DU1RJlIQg3QPzvCWwb0XtOREAZho/CBOUySJrOTGP7Db3dJkjMyXytSL2GNEg4drKyu9m+DH3F2IjJUytpmA6/gfixMzU1MkXQ6+6DcttuMSOM93uR3d3nDwbegnR2Io/Fb8nJiLIKPhY6/BjN44jPUxCPLrNArFvYjLcRy/oZFiggZhirqawFxKYikyFXATHDWE1lLSA2FZkMuQqIGcZqKmsBsanIZMhVQMwwVlNZC4hNRSZDrn8AkCg0K6HJXQAAAABJRU5ErkJggg==\" style=\"width: 56.5px; height: 18px;\" width=\"56.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49px 8px; transform-origin: 49px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA3cAAAAlCAYAAADhnRB3AAAYPklEQVR4Xu1d2eu+RRXXP8A06ypKvrRciEGhpWALJJRREEVKZV0Ihq0ERotmEWGLLSh4USoJEmGLele2gUKGZKUkKF60IF541Wb+AXU+8R48jTNzzmzPM8/znheG3+/7vrOc+XzOmTlnZp55Tj3FP46AI+AIOAKOgCPgCDgCjoAj4Ag4AptH4NTN98A74Ag4Ao6AI+AIOAKOgCPgCDgCjoAjcIoHd64EjoAj4Ag4Ao6AI+AIOAKOgCPgCOwAgVxw95lE/x6g73+zg77P0oVZcJ5Fjll4yckxC1bvJSHPigj6JH33wy0AuaCMs2A1ixwLQl/d1CxYzSJHNZALFpwFq1nkWBD66qZmwer11IMLE734RnXv9llwFqxmkWOfLD/bq2Kcc8Hdf6jeP1D6e4Da7e44dtWjn0dqO5++u57SkgOa822ndRbOIMfLKf05EP0h+vtae3eOIudXqJfnBT1l7N66IALOmR1s58yO1Sw5nbNZmLDLMQtnWDS9mtLvIqIvOUbbkVsvJwLyy4PmX0B/v4bSkifynLNldKCYby24ewPJ7bt0y5AnW4EDeO8KwZ3zXc/1Gpyt0WY9QvOVxMR0EaUlHQfnrE0PnLM2/NYo7ZytgXpbm2twtkabbSjNVRq7O/evENwtPYfOhfp60mT5HhncvYr6/Mh6/X5Oyy+lb56mFO5E5kQEePg8U9EXtPeiQ/nSAHkNBxA7d6XBnezj44XYLqEa0MGLKZ0cGvsJ/XtPpuGtcVarJ6zXM3IGeiDfU5T+alASrFaefchX2p81nIlaziQUrKel44oBTnMWlqFmbDwGztjGYoB+nL7ESuzSH4yHp1XOSaGsJTa6VTt7G3X6lZTOpfQXSj+mtLRP08LZ1uysVk8kRqVzwGgbLPGDJV+hXM+jL15HKXciZ4vBXY1f3uKnzcQ3ZGnxoRcP7jBpfZkSjnSuMYGF5AG8T1H6CKVXGwZnGNh1h/yyrn/SH9dQukXRDtn/hynvyQEHlL2LkiW47OEAlipxSXCHSe8mSi8LGvkF/f1RShanvFQ+a37wdwWlKw/yffaAe06mrXJWoieYZKCD75mQMykSjgh9jtKHFVvDwPZ5SuD7TkqnU4KNf4fSbUYdrHUmrLoYy1fCWaw8xjOMrfic2SJIZVlgxrbFVVjHxmPhjCfdFMQYk5Y8cs9Hp54fCPRV+vsGSpY5qcZGucyW7Iz9BcwJ/6D0TUrWebvSpKLFWjjbqp2V6InkCY+w4HNCCbzhWOfafkiNH4z+fz2jRNri+5aCu1K/HLD08NN62qisq5TvHj70YsFdKOyPDmSMAlOrNxakacEdO07hJCjbwoSYWj35Nv0GBzPM8yH67mZKCH7eT0mbTFsdQA2b2O/W4I6d71QbcPRw7nuNAA8BzN2UEHRaA80tc2bVE+ByHyU4K7ceiLv0wBP+BGevMOhljV6VlJFOcS64w0D6g4g9oZ9/PPTHooMlzkRJP3J5rZyl6kB57EaDs6WDO7YVBNBPUDqhBC54vMwFLcfEGXMU4xA7QG+htNT4+Hth5zF5rHMSl7XaqGxrK3YGHYWOQ59rA98e40QLZ1u2M6ue8HyGIC70p/g38GCZA3rwJeuo9YPhr/5JjKWhXLBT7fGBLQR3NX45sOjlp83Ady8fepHgDsLihj58EMTgs2Zwx8cpHiU5viQmNy24w6SMSxawI8C3DWKwQHCGoI0/b6f/hMf7OIDD5H0BpTCA4wk/Fxxy/a0OYI0CW4I7ViY4d9+iBAcFxvpmStit5Z087Cy8tkaIhjI8qaEK68S8dc4sesKTRmzXWWK29G5CSHU4uaWCOw7gUD5mz7z6adFBqzPRoJbPKWrhLNWeXNldOrhjrKAn8mgaeEOf4EilFgmOiTMeI7W5pqdOafoCW+LdJyxgXkLpakoclFvmJLRhtdFQni3YGTuPkP19lNa6bZhtvIazrduZVU9wgRh8jZgfBv54Xoefgh28pT4tfjCfiIj5jlb5Zw/uav3ynn6aFUtLvhq+e/rQiwR3EggECfisGdxJeaRDlJtwoXjfp/QmSrFz9bKesG9y0ktNlNKR1ib+FgfQopSxPJbgDiuKSLEBM5z4tT7WyhkrJ1eTrSvRe+DMoifQWzxrmjpOzBPl2vaKvvyLEh8bTQV3vEiSCt7gvGKBBR/taKfVmeipqxbOcjoOnoDRksEdB3BYOY6dOtDGtmPiDEEBHM+lF7dCnQFnf6OUClTkmGnVJauNhrLMbmdybrcGuj3HBK6rlbOt25lFT7QAFliyblv1egSXpX4wTtUgGG255Xr24E7ibPXLe/tpI7hGnVa+e/rQHtwR8HyOORdwYFLG0bWUE8wDL4gMBw1eWcBvqdUk6XRqE0itA9iiuFpwx0cecytLcrtZc6xbZJVlpfGXHAndA2cWPUE/c8+Jluwo9+IsrAcyfpoSjqvlAjM5sedsiANWbffO4kz07rOFs5ij/iB9yUdqMZ4t6bjwhQWpC1ykMxUehTomzniMh5N2B6U1L7yBTWGhEoF36iOP/2mLcVYbjbU1s53JIFcbL3qPBbFxsJazPdiZRU8kXylfi/NgLsFJrDU+VmcfsvHiGHym31KqvbRnj8Fdbz9tlC5Y+O7tQ3twR2xagjscy+CjhikFSD3vIidJrNqmnqfA6gyOwmiDTo0D2Kq0WnCHnc2XUMoFCjXPY7TKLY/TaEGzbGsPnPXQEw6ENOeuladUeXZK+GFxHiRjiwNy8SB3dAoLNbwDmLNHizPRu981nKE/Z1DCzhmveC4Z3GkYsHMS2/09Js7kWMSYAZPvUQqP8WuYtv4OPXmAUi7AtK6el9hoTO6Z7YzHP8idChZaubCWb+FsD3Zm0RO5yI5gPHaagLEo8QesHFnzWZx9rkvqIL7D2I4xH75WSaC3x+Cut59m5a80n4Xv3j60B3fEkiW4s5DJwV34cCsTqzlcXB5t5ZzOGgfQIn8ujxbcWeqXwZ12s5OlPi2PHOglprzTkLtOfw+cteoJ87XWJMjH/XDbJd8emAvupP3kglHptOaCQIszoelg6e+lnCFwwvOsfAnHjMEd+oQV8ndHnJFj4UyezIjpBBxRLDgsdZGKRS+lLqUuVCq10Vi7s9oZnK2fHgSWC64YF/GZ7Vp9yJTibA92ZtUTuYgSPoYhLw9b8uKiUO8tzj7KyCPtMdvBKYAvUNIu4UPZPQZ3vf00y7hYk8fKt1Z3iQ/twR2h2Su44xUWuasgj0OUBHe5VcJSB1BTGMvvPYI7HqhSl8pY5CjJI7fs0SaOrV1NSd52iu9xnbXccdwLZy16wpMgrpFe8lp2yS9WWM+jJG88ywV3vPONOqzBXS5wtToTJTqp5S3hjG/v/QBVyjs/swV3cLTgRKUcqWPijN9T9WLC440Hx02ORSXHxjU96vE7O8m5521LbTQm16x2Jnf4gQF0VV6chr4gKL+K0ppHbCWmKc72YGdWPZGXOAEb2NU7KOFdcLg3AbxaA6IedhSro8TZ53ednUMV4Vhu7HVFllvW9xbcjfDTZuA7J0OJD+3BHSHZI7jjldnwKuuSB9Pl6lrumbQSB7CXsvYI7njiWermRTk5AwescuFF5f+mBAdL3uApnfy9cFajJ3xbnnyfjvV20V66hnpSFxjlgjv+DeWtwV3OcbU6Ez37XcJZ7OHrWYI78CdvIsa4eHnECT42zqSu8Ds3pa1ZrjTvqW+5unixMnXKosZGY+3NamcyIILcmLdwlBWfCynJhcK1j2wyrinO9mBnJXoSBnjAB0GeXAhbyo5i7ZQEd2F5zNGYk2WQZ/Gp9hbcjfDTRulEC99SphIf2oM7Qq5HcMdOVRiUSQXUbhyUx8X2FtzxxSaYMFuu8y0xPnkeO4ZnOAHwBL0XzkoCBeCKVSE44MAFF1/Ij/WW0RJ+UnlZV3DranjluCW403bIrfyWOBM9+o06rJxBNryLMHymZO3gjl8+i3/PpxS+EzR0gq3HavbAWUpHeJecsVriyLqmr4x3as6qtdFYuzPaWXikP7ZYFPL2Quqc5Xichn3t7znO9mBnpXqSCvBSN57X4l5TroezL49sYs7T3kW75+Cul29dw6WlTA++S31oD+6ImdbgjkHHSzPDF0lKp0RblbXeJml1AC1KZ83TunPHTueSjouc0FIvLJXPVTA/e+GsRU9iuwpL3XAKufHaA0xe4cca3OUmOsn5FnfuWD9z7/HTAlyr3bfmg6w3UuLFgvBItrTRPXOm4Sh10rIKr9XX+js/J5k6Tltro1sJ7uQckLslU87Za/OW42wPdlYa3LHPgV0uHKeVC01r77T2cPZhS1L/NN9qz8FdL9+6ddxMle/Bd6kP7cFdh+CO310Uu5lpxNZxi9Neq7wtwR2fjV765a/W1cpw4jubQLr/AJTmJM98lLaHnsSC31odspTjK9VTu7uW4A7t7PVYJoJuvPYgfE6UsV175y7FsdxFl07IHo6L9bAz4MZH6rRVaIsdteSBDX6NUmqHo8VGtxjc5fgoWQhs4UQrq3G2BzsrCe74+BoHcThJgO8uFkBqwZCGecvvPZx9tF/y3tY9B3e9/LQWTnNlW/mu8aE9uGsM7niii90Ex2RbgwzrjVa9nIkSRa4N7tgZxQTZ8gLOElk5Lz8zUWL4HBTsgbNeesKOuYZjDUeyDA9g2CF8LFEZB91Yjf3ZIQ/femq1H+vx5xJnorXvXF7jjBeScIlD7HMZfYlVar5EgPOsfeGDXCSQO8DHwJlVN3gVfs3gjm0wtbPRaqMxLGa0M3lZg8aHda6w6kFpPo0z1LcHO7PqCY/vMd446AMm2iunSnkoyd/q7Mu2eH7WTtbsLbgDBlbbs+p/CYcleVv4rvWhPbgjhmqPZeLYGC7lyAV2UABekdWcY1ZA7dY0zQEsUTpr3prgjs+8/5IaWTqwkxOadh49Zvh74KyXniy1GySDLqteIh9PanLitu7c5Y7nWJ2JElm1vBpncgVeq4t/18Ydaz2t+WK7rsfAmRU31n9c/ITnTZf+8DNkuUsnWm001qcZ7Uw6jtqRL6uDOYJPC2dodw92ZtUTXtRNje3yorW1du9anP1Qj9h/0U5G7TG46+2njbBROZZoC0Vh+y0+tAd3hGZNcGcN7EoGVjb43Bl/Dlrupf8seUV9aXDXopS9DEyeR885+zKo5ud+rJPhzJxpgYIV59xKqLUOSz6+0CWXl4/VYNUVAzs+N1G6h5J8wFy7kAj1aIsoVmfC0jdrHo0z/J774H1yeEcmPnBK8Uk9v2iVqVc+thVpi8fAmRU/Hq80J81aX0k+a5DQaqMxmWa0M8hpPbHAeq0FgSV8WPJaOUNde7Azi57IY7KpOV/uymq7XRYeavL0DO5YT3PvRoaMewzuevtpNVxaytTw3epDe3BHzJQGdzhiBIcyt2OHAeQZSngprRxwUhN3yYCjOYAWZSvNUxrcYcDRduyAI5zyUR+Jac5h4tUfGVTvgbNeehI+vzCKL0u9uWfu+GIjPDif2/3glV1tFc3iTFhkLsnTytlSu6wlfUJefjYkXLhyzp5FEuPQmZRSlz+VYm7NH3tfYliW39FnOd6bs9GYTLPamXxPaspxls885d6ZaeXCmq+Usz3YmUVPLMEdMC7VUSsv1nw1zn6s7tS4Gsu7x+Cut59m5a80Xw3frT70tMEdBqNLKJ1OCStij5Siacwvj5nkdne4Ol4tw0sxUxMdR9x4DwmCO3x4dyi1usertpYXfKccwJGYlQR3CAYw6IQ3h0pKsJKIF/ny8aNRsvOqVmo3VF55HQaAS3AGTIDFWZQepdQz2G0NFCCbvAk29qLUUbKnzFeblGVwE7t9UT77pdl7zpkY1e9WzizB3SjZc0MuyxU7KnUMnPGLiB8nkGLX5fPOSurGxVGc8Vx1J8mVOwmCMf3XlMJXk8Q412w0LDOrncm5IRW4yfEkDABn42wpO4NTifcAPknpVwl9z40Vqd8swR3K8uJdakFX8hpyNkr2sE9WZx/+5mmUUr4mL7xajpfmnP1R/bZyFhsTrJsuLX7aqH7X8s3lanzosM1pgzu53QqhNUesZrBAmZLgjgM7BGCYDFOfK+kHrMLK4IZX2rCrEPZFrqpZjDTlAI7EzBrcsQyYDJ9OAHRC3+PSB9nXUbJrKzvMfyzoXoIzeVwGcPU8JmIJFDj4Rf8RaPNiBGRhxw86G9ulHil7yrYsjmPuAXOeCCzXlqcmppH9tnCWG+u04G6E7Ozg4pjrNZRuCQTkNnM7G3vmTJ4gAEbh+xt5XsFJh49RCoO/EZxJ+4aDe31GqS6i386npL1Hi6uw2KhsbmY7k/5BbPcuNZ7MytloO5M7meBYOx2RG8vC36yBAnOGBd3YDea8IxvKNlL2sC+W4E7uHMPnDOdgbUEobDPl7I/st5WzGNfW4K7WTxvZ7xq+uUytD23l+3/5Ts1YntXZDwdxJgzKmnqHDsrIh17x94iHzEEuJlR+RiXn8PEEHL6UNwVRbIWa60AZvmYaMmCQwVEc67tXUg7gSMwsfIcBWm7gDnfSRsqOQRCygTus5vFqohzkY04V5B/NmRzA0V7PG7wsgQIfSWWuYGdPUMKOOXaeoZs3UIrtNoyUPaU7FsdRvryWV2/x3XWUsKhgPT6VmphG9tvCWc6utOBuhOyhIwsdvvUg5LmH8fWL9G9uV3rPnMnFO+YOiyl4bvrkoJO5RZ0RnEm8c/rEv1ltBvktNirbnN3O+FQN30CLXRQ5nsT8hlk5G21nciGDOdaeBbPoH/KUBArMGfyMD1Lik1/8yojYQspI2UN9t/jBcmGay/P8jAUXPF/9CWVcle2mgruR/S7hjGUt8cu5TI2fNrLfNXyjTIsPHdrRIjt3mPzfSemMiBVjgosduwTwWAVGGawawvnvdYMYlOcKSudF5MHOBQaCcPUZ7cfkjw1MuMAgFSzw8UMEd6gPee+jhIBD7prE6uXvUg7gSMy04A6r9xhorJ/bD5xy/pGyo40Qd3wH3XuAkvYcyUjO2EmATmKwxof/tWKZymcJFGK2AFwsR2pGyp7rE37jS1RyGGHcwdFf9JH5LjninZqYRvbbwpnW58spQ+oSlVGyh2M8xrInKJXgjX7tlTMeQ94lyHvoYGd30b+xxRPOOoIz1m3rGIMAxvpoBHTYaqPItwU7wxiCx0TgVOMD+3qYEriLzduzczbKziSfwACL1msEd5Aj5AzfaXM+62Jv2XlsK/WDc/Oz5Yi0tO+csz+q3yXBXY1fLvtX46eN6ncN360+dDiWLxLcWSeQVD5MFrdTKlXm1nZnLW9xAHtjpgV3PbHqLXtP2WrrsnCGgeaEUq9FDEubtf0Jy/WWvZdcLfVYJqbe/XbOWhizre47Z20Y9y7tdtYb0fH1WTiDcwm/rddipaXNXj3vLXsvuVrqsVyo0rvfS3LWik1PXW2RpVfZ6YM77OjcTekCSrnVzV6AbKEezQEcgdlSwd0I2WfgVOMMq04PUoo921Yrv9Zmbb1huRGy95KtpR5tYhrRb+eshTE9uHPO2vAdUdrtbASqY+vUOEPrWIzHqaTwFFStZJY2a+sOy/WWvZdcLfVYgrve/V6SsxZseve7RZZeZacO7uDof5eSPDPdq+NbrifnAI7CbIngbpTsM3Cd44yfg9CeSyrtxxKBwijZS/s6In9uYhrVb+esjUnnrA2/NUo7Z2ug3tam5rTj2SE8o3htWzP/V1prs1dTI2TvJVtLPVpwN6LfS3HWgsuIfrfI06tsU3CHh8AfCyR5iv62PjuW6wScp09Suq1Tfb0AW7oeEBR+bqQvYldXj8QMwZ3zbWO/hDPUiAHQ8uyfrfVncyFQgC3eERR8hv62Pj+jtTlKdq3d3r/zldOy3svoj9QrPUb12zmzM+uc2bGaJadzNgsTdjlKOcPzfPj0fowGY+6llK6KiK49N2/t7SjZre33ysevXpH1nUN/3EwpdlHiqH4vwVkLZqP63SJTTdlSvtXbMmNCWK4YrxH+WMvwzWNh/5fGeRY5tqAHs2CFQOHiCGCpdy1uAdtRMs6C1SxyjMK5Z72zYDWLHD2xHVXXLFjNIsconHvWOwtWCBT4lsmwf7mb3XtisZW6ZsFqFjm2wlutnMU4u8HUQu3lHAFHwBFwBBwBR8ARcAQcAUfAEZgIAQ/uJiLDRXEEHAFHwBFwBBwBR8ARcAQcAUegFgEP7mqR83KOgCPgCDgCjoAj4Ag4Ao6AI+AITISAB3cTkeGiOAKOgCPgCDgCjoAj4Ag4Ao6AI1CLgAd3tch5OUfAEXAEHAFHwBFwBBwBR8ARcAQmQuC/KnxKvNDivuAAAAAASUVORK5CYII=\" style=\"width: 443.5px; height: 18.5px;\" width=\"443.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with rotations not allowed. Hence, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 74.5px; height: 20px;\" width=\"74.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106.5px 8px; transform-origin: 106.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that will calculate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 42px; height: 20px;\" width=\"42\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62px 8px; transform-origin: 62px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96px 8px; transform-origin: 96px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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style=\"width: 122.5px; height: 45px;\" width=\"122.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we are given:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36px 8px; transform-origin: 36px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" style=\"width: 667.5px; height: 45px;\" width=\"667.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function sfr = countFRecs(n)\r\n    sfr = 31;\r\nend","test_suite":"%%\r\nn = 6;\r\ns_correct = 31;\r\nassert(isequal(countFRecs(n),s_correct))\r\n%%\r\nn = 10;\r\ns_correct = 324;\r\nassert(isequal(countFRecs(n),s_correct))\r\n%%\r\nn = 15;\r\ns_correct = 5094;\r\nassert(isequal(countFRecs(n),s_correct))\r\n%%\r\nn = 20;\r\ns_correct = 55710;\r\nassert(isequal(countFRecs(n),s_correct))\r\n%%\r\nn = 25;\r\ns_correct = 521566;\r\nassert(isequal(countFRecs(n),s_correct))\r\n%%\r\nn = 30;\r\ns_correct = 3668686;\r\nassert(isequal(countFRecs(n),s_correct))\r\n%%\r\nn = 35;\r\ns_correct = 26992462;\r\nassert(isequal(countFRecs(n),s_correct))\r\n%%\r\nn = 50;\r\ns_correct = 8826106702;\r\nassert(isequal(countFRecs(n),s_correct))\r\n%%\r\nns = 1:75;\r\nys = arrayfun(@countFRecs,ns);\r\nss = mod(floor([sum(ys) nnz(ys) mean(ys) mode(ys) median(ys) std(ys)]),1e10);\r\nss_correct = [1887919459 75 558505592 1 86618830 6857256509];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('countFRecs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2022-08-25T10:10:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-24T08:52:23.000Z","updated_at":"2026-03-28T13:19:26.000Z","published_at":"2022-08-25T10:06:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI'll celebrate my comeback to Cody with this one easy problem...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e----------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe rectangle below is special:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"142\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"182\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIts area is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e40,320\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e which equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. We call such rectangle a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efactorial rectangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which is an integer-sided rectangle with an area equal to a factorial number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, we want to know how many are these factorial rectangles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we define the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_{FR}(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the number of factorial rectangles with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en!.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e The factorial rectangles with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5!=120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1,\\\\ 120],\\\\ [2,\\\\ 60],\\\\ [3,\\\\ 40],\\\\ [4,\\\\ 30],\\\\ [5,\\\\ 24],\\\\ [6,\\\\ 20],\\\\ [8,\\\\ 15],\\\\ [10,\\\\ 12]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with rotations not allowed. Hence, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_{FR}(5)=8.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that will calculate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{FR}(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{FR}(n) = \\\\sum_{i=1}^n C_{FR}(i)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we are given:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{FR}(6) = \\\\sum_{i=1}^5 C_{FR}(i) = C_{FR}(1)+C_{FR}(2)+C_{FR}(3)+C_{FR}(4)+C_{FR}(5)+C_{FR}(6) = 1+1+2+4+8+15 = 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Sequences 69: Radix Economy of Factorials","description":"The Radix Economy of a number in a particular base is the number of digits needed to express it in that base, multiplied by the base. In functional form we write: , where  is the radix econony,  and , are the base and number, respectively, and , is the number of digits of the base- representation of .\r\nFor example, if  and , then the radix economy is :\r\n    \u003e\u003e E = 2 * length(dec2bin(1000))\r\n    \u003e\u003e E =\r\n        20\r\nGiven a base , and an integer , calculate , for .\r\nFor example, if  and , we have:\r\n    \u003e\u003e F = 3 * length(dec2base(factorial(10),3))\r\n    \u003e\u003e F =\r\n        42\r\n----------------\r\nNOTE: As it is, this problem is quite simple. In fact, a solution is already given for small values of  and . Therefore, to make it a bit interesting, some built-in functions are disabled.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 378px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Radix_economy\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRadix Economy\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e of a number in a particular base is the number of digits needed to express it in that base, multiplied by the base. In functional form we write: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"137.5\" height=\"20\" style=\"width: 137.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eE\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is the radix econony, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, are the base and number, respectively, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41\" height=\"20\" style=\"width: 41px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, is the number of digits of the base-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e representation of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64\" height=\"18\" style=\"width: 64px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, then the radix economy is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47.5\" height=\"18\" style=\"width: 47.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; E = 2 * length(dec2bin(1000))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; E =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        20\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, and an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, calculate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"113.5\" height=\"19\" style=\"width: 113.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; F = 3 * length(dec2base(factorial(10),3))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; F =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        42\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e----------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e As it is, this problem is quite simple. In fact, a solution is already given for small values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Therefore, to make it a bit interesting, some built-in functions are disabled.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = F(b,n)\r\n    f = b * length(dec2base(factorial(n),b));\r\nend","test_suite":"%%\r\nb = 3; n = 10;\r\nf_correct = 42;\r\nassert(isequal(F(b,n),f_correct))\r\n%%\r\nb = 20; n = 15;\r\nf_correct = 200;\r\nassert(isequal(F(b,n),f_correct))\r\n%%\r\nb = 2; n = 100;\r\nf_correct = 1050;\r\nassert(isequal(F(b,n),f_correct))\r\n%%\r\nb = 50; n = 50;\r\nf_correct = 1900;\r\nassert(isequal(F(b,n),f_correct))\r\n%%\r\nb = 7; ns = 1:10;\r\nfs_correct = [7 7 7 14 21 28 35 42 49 56];\r\nassert(isequal(F(b,ns),fs_correct))\r\n%%\r\nb = 30; ns = randi(15,1,100);\r\nfs_correct = arrayfun(@(n) b * length(dec2base(factorial(n),b)),ns);\r\nassert(isequal(F(b,ns),fs_correct))\r\n%%\r\nb = 123; ns = 1234:5:6789;\r\nfs = F(b,ns);\r\nss = floor([mean(fs) median(fs) mode(fs) std(fs)]);\r\nss_correct = [757044 748393 193110 338413];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('F.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java') ...\r\n|| contains(filetext, 'log') || contains(filetext, 'sum') || contains(filetext, 'prod') || contains(filetext, 'if') || contains(filetext, 'for') ...\r\n|| contains(filetext, 'arrayfun') || contains(filetext, 'cellfun') || contains(filetext, 'solve') || contains(filetext, 'root') ... \r\n|| contains(filetext, 'mean') || contains(filetext, 'while') || contains(filetext, 'bsxfun') || contains(filetext, 'repmat') ...\r\n|| contains(filetext, '^') || contains(filetext, 'gamma');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":255988,"edited_by":255988,"edited_at":"2022-09-02T20:38:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2022-08-31T09:34:30.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2022-08-30T05:42:22.000Z","updated_at":"2026-03-28T13:51:27.000Z","published_at":"2022-08-30T20:16:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Radix_economy\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRadix Economy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of a number in a particular base is the number of digits needed to express it in that base, multiplied by the base. In functional form we write: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE(b,N) = b\\\\  \\\\cdot \\\\ C(N_b)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radix econony, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, are the base and number, respectively, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(N_b)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the number of digits of the base-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e representation of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN=1000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then the radix economy is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE=20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e E = 2 * length(dec2bin(1000))\\n    \u003e\u003e E =\\n        20]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, and an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, calculate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(b,n)=E(b,N)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN= n!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e F = 3 * length(dec2base(factorial(10),3))\\n    \u003e\u003e F =\\n        42]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e----------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e As it is, this problem is quite simple. In fact, a solution is already given for small values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, to make it a bit interesting, some built-in functions are disabled.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially completed groups","description_html":null,"image_location":"/images/responsive/supporting/matlabcentral/cody/badges/problem_groups_unknown_2.png","bonus":null,"players_count":0,"active":false,"created_by":null,"updated_by":null,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"created_at":"2018-01-10T23:20:29.000Z","updated_at":"2018-01-10T23:20:29.000Z","community_badge_id":null,"award_multiples":false}}