{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":56593,"title":"List the nth term of Rozhenko’s inventory sequence","description":"Consider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\r\n0\r\n1, 1, 0\r\n2, 2, 2, 0\r\n3, 2, 4, 1, 1, 0\r\n4, 4, 4, 1, 4, 0\r\nWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19th term is 4. \r\nThis sequence produces interesting plots and music. See the related Numberphile video for more. \r\nWrite a function to report the th term of this sequence. ","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: 345px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 172.5px; transform-origin: 407px 172.5px; vertical-align: baseline; \"\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: 374.6px 8px; transform-origin: 374.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\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: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e0\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: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1, 1, 0\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: 27.2167px 8px; transform-origin: 27.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2, 2, 2, 0\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: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3, 2, 4, 1, 1, 0\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: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4, 4, 4, 1, 4, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\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; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; 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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\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: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e term is 4. \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: 112.425px 8px; transform-origin: 112.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis sequence produces interesting \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A342585/graph\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eplots\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: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/play?seq=A342585\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003emusic\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: 18.275px 8px; transform-origin: 18.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. See \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=rBU9E-ZOZAI\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ethe related Numberphile video\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: 31.8833px 8px; transform-origin: 31.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for more. \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: 90.1px 8px; transform-origin: 90.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to report 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: 78.5583px 8px; transform-origin: 78.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Rozhenko(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 19;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny_correct = 5;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 347;\r\ny_correct = 25;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 823;\r\ny_correct = 27;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 1997;\r\ny_correct = 20;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 4721;\r\ny_correct = 68;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 13859;\r\ny_correct = 18;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 19793;\r\ny_correct = 7;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 24677;\r\ny_correct = 51;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 41903;\r\ny_correct = 357;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 25537;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(Rozhenko(Rozhenko(n))),y_correct))\r\n\r\n%%\r\nn = [1 4 8 14 20 28 37 46 57 69 82 95 110 125 142 159 177 196 216 238 260 285 310 335 362 390 418 448 478 511];\r\na = arrayfun(@Rozhenko,n);\r\ns_correct = 0;\r\nassert(isequal(sum(a),s_correct))\r\n\r\n%%\r\nfiletext = fileread('Rozhenko.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-13T14:07:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-13T04:07:55.000Z","updated_at":"2026-01-24T12:19:36.000Z","published_at":"2022-11-13T04:08:12.000Z","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\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\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\u003e0\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\u003e1, 1, 0\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\u003e2, 2, 2, 0\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\u003e3, 2, 4, 1, 1, 0\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\u003e4, 4, 4, 1, 4, 0\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\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e term is 4. \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\u003eThis sequence produces interesting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A342585/graph\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eplots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/play?seq=A342585\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emusic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=rBU9E-ZOZAI\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe related Numberphile video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more. \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\u003eWrite a function to report 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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\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 term of this sequence. \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":60739,"title":"Explore the twin prime Goldbach conjecture","description":"The Goldbach conjecture says that every positive even integer greater than 2 can be expressed as the sum of two prime numbers in at least one way. For example, 16 is 3+13, 48 is 5+43, and 210 is 19+191. In these examples, the prime numbers are twin primes, or prime numbers that are 2 away from another prime—for example, 3 and 5, 11 and 13, 41 and 43, 17 and 19, and 191 and 193. \r\nIn fact, as far as we know, all but 35 even numbers can be written as the sum of twin primes. This statement can be called the “twin prime Goldbach conjecture.” The exceptions have an interesting pattern, especially if zero is allowed. \r\nWrite a function that takes an even number  as input and produces all pairs of twin primes that sum to . The output should be a two-column matrix with the smaller of the pair in the first column and sorted by the first column. For example, the input 16 should produce [3 13; 5 11]; notice that [11 5] and [13 3] are not included. If the number cannot be written as the sum of twin primes, return [].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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 solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 228px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114px; transform-origin: 407px 114px; 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; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Goldbach conjecture says that every positive even integer greater than 2 can be expressed as the sum of two prime numbers in at least one way. For example, 16 is 3+13, 48 is 5+43, and 210 is 19+191. In these examples, the prime numbers are twin primes, or prime numbers that are 2 away from another prime—for example, 3 and 5, 11 and 13, 41 and 43, 17 and 19, and 191 and 193. \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-collapse: preserve; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn fact, as far as we know, all but 35 even numbers can be written as the sum of twin primes. This statement can be called the “twin prime Goldbach conjecture.” The exceptions have an interesting pattern, especially if zero is allowed. \u003c/span\u003e\u003c/span\u003e\u003c/div\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; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an even number \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; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as input and produces all pairs of twin primes that sum to \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; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The output should be a two-column matrix with the smaller of the pair in the first column and sorted by the first column. For example, the input 16 should produce \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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[3 13; 5 11]\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; notice that \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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[11 5]\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[13 3]\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not included. If the number cannot be written as the sum of twin primes, return \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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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: 0px 0px; transform-origin: 0px 0px; 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 = twinPrimeGoldbach(n)\r\n  p = primes(n)-2;\r\n  y = sum(p);\r\nend","test_suite":"%%\r\nn = 8;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [3 5];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 16;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [3 13; 5 11];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 76;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [3 73; 5 71; 17 59];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 888;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [5 883; 7 881; 29 859; 31 857; 59 829; 61 827; 227 661; 229 659; 269 619; 271 617];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 4562;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [13 4549; 43 4519; 139 4423; 433 4129; 643 3919; 1021 3541; 1033 3529; 1093 3469; 1231 3331; 1303 3259; 1873 2689];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 69420;\r\ny = twinPrimeGoldbach(n);\r\nprod_correct = [1179851 1318619 15706811 15844739 18601619 18739379 35896379 36033131 41223779 41360219 101016371 101149259 235769459 235893971 300398771 300519059 320138051 320257019 335772659 335890571 406099979 406213019 488632979 488740019 495999971 496106459 692259779 692350331 716418299 716506691 725655779 725743331 729849251 729936419 765755891 765839699 779228459 779310971 859902059 859976339 861682571 861756659 935069171 935134859 971214011 971275139 981012419 981072251 985122059 985181339 1004250179 1004306819 1006791059 1006847339 1010488379 1010544131 1017121499 1017176291 1033200299 1033252691 1050055379 1050105131 1061479259 1061527139 1076165819 1076211179 1086431459 1086474971 1148968259 1148998139 1163400611 1163426339 1167096779 1167121331 1189892219 1189907651 1192330259 1192344371 1195885811 1195897739 1196587331 1196598779 1197745691 1197756299 1203589451 1203593819 1204004411 1204007939 1204666451 1204667819]';\r\nassert(isequal(prod(y,2),prod_correct))\r\n\r\n%%\r\nn = 777774;\r\ny = twinPrimeGoldbach(n);\r\nprodsum_correct = 10687098646246;\r\nassert(isequal(sum(prod(y,2)),prodsum_correct))\r\n\r\n%%\r\nn = 53942456;\r\ny = twinPrimeGoldbach(n);\r\nans_correct = 4445;\r\nassert(isequal(size(y,1)+find(y==27237733),ans_correct))\r\n\r\n%%\r\nn = 165324896;\r\ny = twinPrimeGoldbach(n);\r\ns = sum(y(:,2)./y(:,1));\r\ns_correct = 3.257362846413793e+05;\r\nassert(abs(s-s_correct)\u003c1e-8)\r\n\r\n%%\r\na = [];\r\nfor n = 2:2:10000\r\n    y = twinPrimeGoldbach(n);\r\n    if isempty(y)\r\n        a(end+1) = n;\r\n    end\r\nend\r\na_correct = [2 4 94 96 98 400 402 404 514 516 518 784 786 788 904 906 908 1114 1116 1118 1144 1146 1148 1264 1266 1268 1354 1356 1358 3244 3246 3248 4204 4206 4208];\r\nassert(isequal(a,a_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-09-24T02:15:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-09-24T02:15:46.000Z","updated_at":"2024-09-24T02:15:56.000Z","published_at":"2024-09-24T02:15:56.000Z","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 Goldbach conjecture says that every positive even integer greater than 2 can be expressed as the sum of two prime numbers in at least one way. For example, 16 is 3+13, 48 is 5+43, and 210 is 19+191. In these examples, the prime numbers are twin primes, or prime numbers that are 2 away from another prime—for example, 3 and 5, 11 and 13, 41 and 43, 17 and 19, and 191 and 193. \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 fact, as far as we know, all but 35 even numbers can be written as the sum of twin primes. This statement can be called the “twin prime Goldbach conjecture.” The exceptions have an interesting pattern, especially if zero is allowed. \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\u003eWrite a function that takes an even 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\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produces all pairs of twin primes that sum 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:t\u003e. The output should be a two-column matrix with the smaller of the pair in the first column and sorted by the first column. For example, the input 16 should produce \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3 13; 5 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e; notice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[11 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[13 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are not included. If the number cannot be written as the sum of twin primes, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\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\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":60331,"title":"Compute the area of a Q","description":"A figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \r\nWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \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: 477.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 238.85px; transform-origin: 407px 238.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; 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: 380.408px 8px; transform-origin: 380.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \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-collapse: preserve; 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: 316.85px 8px; transform-origin: 316.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; 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 166.85px; text-align: left; transform-origin: 384px 166.85px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Qarea(a,c)\r\n  y = a*c;\r\nend","test_suite":"%%\r\na = 1;\r\nc = sqrt(2);\r\ny = Qarea(a,c);\r\ny_correct = 2.121320343559643;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 2;\r\nc = sqrt(5);\r\ny = Qarea(a,c);\r\ny_correct = 5.031152949374527;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 5/2;\r\nc = sqrt(7);\r\ny = Qarea(a,c);\r\ny_correct = 7.011240974321167;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 3;\r\nc = sqrt(8);\r\ny = Qarea(a,c);\r\ny_correct = 8.013876853447540;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 3;\r\nc = sqrt(11);\r\ny = Qarea(a,c);\r\ny_correct = 11.055415967851332;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 4;\r\nc = sqrt(19);\r\ny = Qarea(a,c);\r\ny_correct = 19.070182877990447;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 5;\r\nc = sqrt(23);\r\ny = Qarea(a,c);\r\ny_correct = 23.019991311901052;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = sqrt(27);\r\nc = sqrt(29);\r\ny = Qarea(a,c);\r\ny_correct = 29.018512609609640;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 6;\r\nc = sqrt(31);\r\ny = Qarea(a,c);\r\ny_correct = 31.086684359134285;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = sqrt(43);\r\nc = sqrt(41);\r\ny = Qarea(a,c);\r\ny_correct = 41.011626258563474;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('Qarea.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-18T15:50:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-18T03:49:34.000Z","updated_at":"2026-03-04T13:41:21.000Z","published_at":"2024-05-18T03:49:49.000Z","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\u003eA figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \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\u003eWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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the nth term of Rozhenko’s inventory sequence","description":"Consider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\r\n0\r\n1, 1, 0\r\n2, 2, 2, 0\r\n3, 2, 4, 1, 1, 0\r\n4, 4, 4, 1, 4, 0\r\nWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19th term is 4. \r\nThis sequence produces interesting plots and music. See the related Numberphile video for more. \r\nWrite a function to report the th term of this sequence. ","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: 345px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 172.5px; transform-origin: 407px 172.5px; vertical-align: baseline; \"\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: 374.6px 8px; transform-origin: 374.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\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: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e0\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: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1, 1, 0\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: 27.2167px 8px; transform-origin: 27.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2, 2, 2, 0\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: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3, 2, 4, 1, 1, 0\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: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4, 4, 4, 1, 4, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\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; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; 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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\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: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e term is 4. \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: 112.425px 8px; transform-origin: 112.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis sequence produces interesting \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A342585/graph\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eplots\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: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/play?seq=A342585\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003emusic\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: 18.275px 8px; transform-origin: 18.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. See \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=rBU9E-ZOZAI\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ethe related Numberphile video\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: 31.8833px 8px; transform-origin: 31.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for more. \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: 90.1px 8px; transform-origin: 90.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to report 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: 78.5583px 8px; transform-origin: 78.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Rozhenko(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 19;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny_correct = 5;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 347;\r\ny_correct = 25;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 823;\r\ny_correct = 27;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 1997;\r\ny_correct = 20;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 4721;\r\ny_correct = 68;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 13859;\r\ny_correct = 18;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 19793;\r\ny_correct = 7;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 24677;\r\ny_correct = 51;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 41903;\r\ny_correct = 357;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 25537;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(Rozhenko(Rozhenko(n))),y_correct))\r\n\r\n%%\r\nn = [1 4 8 14 20 28 37 46 57 69 82 95 110 125 142 159 177 196 216 238 260 285 310 335 362 390 418 448 478 511];\r\na = arrayfun(@Rozhenko,n);\r\ns_correct = 0;\r\nassert(isequal(sum(a),s_correct))\r\n\r\n%%\r\nfiletext = fileread('Rozhenko.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-13T14:07:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-13T04:07:55.000Z","updated_at":"2026-01-24T12:19:36.000Z","published_at":"2022-11-13T04:08:12.000Z","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\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\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\u003e0\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\u003e1, 1, 0\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\u003e2, 2, 2, 0\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\u003e3, 2, 4, 1, 1, 0\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\u003e4, 4, 4, 1, 4, 0\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\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e term is 4. \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\u003eThis sequence produces interesting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A342585/graph\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eplots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/play?seq=A342585\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emusic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=rBU9E-ZOZAI\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe related Numberphile video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more. \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\u003eWrite a function to report 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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\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 term of this sequence. \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":60739,"title":"Explore the twin prime Goldbach conjecture","description":"The Goldbach conjecture says that every positive even integer greater than 2 can be expressed as the sum of two prime numbers in at least one way. For example, 16 is 3+13, 48 is 5+43, and 210 is 19+191. In these examples, the prime numbers are twin primes, or prime numbers that are 2 away from another prime—for example, 3 and 5, 11 and 13, 41 and 43, 17 and 19, and 191 and 193. \r\nIn fact, as far as we know, all but 35 even numbers can be written as the sum of twin primes. This statement can be called the “twin prime Goldbach conjecture.” The exceptions have an interesting pattern, especially if zero is allowed. \r\nWrite a function that takes an even number  as input and produces all pairs of twin primes that sum to . The output should be a two-column matrix with the smaller of the pair in the first column and sorted by the first column. For example, the input 16 should produce [3 13; 5 11]; notice that [11 5] and [13 3] are not included. If the number cannot be written as the sum of twin primes, return [].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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 solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 228px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114px; transform-origin: 407px 114px; 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; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Goldbach conjecture says that every positive even integer greater than 2 can be expressed as the sum of two prime numbers in at least one way. For example, 16 is 3+13, 48 is 5+43, and 210 is 19+191. In these examples, the prime numbers are twin primes, or prime numbers that are 2 away from another prime—for example, 3 and 5, 11 and 13, 41 and 43, 17 and 19, and 191 and 193. \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-collapse: preserve; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn fact, as far as we know, all but 35 even numbers can be written as the sum of twin primes. This statement can be called the “twin prime Goldbach conjecture.” The exceptions have an interesting pattern, especially if zero is allowed. \u003c/span\u003e\u003c/span\u003e\u003c/div\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; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an even number \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; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as input and produces all pairs of twin primes that sum to \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; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The output should be a two-column matrix with the smaller of the pair in the first column and sorted by the first column. For example, the input 16 should produce \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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[3 13; 5 11]\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; notice that \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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[11 5]\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[13 3]\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not included. If the number cannot be written as the sum of twin primes, return \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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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: 0px 0px; transform-origin: 0px 0px; 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 = twinPrimeGoldbach(n)\r\n  p = primes(n)-2;\r\n  y = sum(p);\r\nend","test_suite":"%%\r\nn = 8;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [3 5];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 16;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [3 13; 5 11];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 76;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [3 73; 5 71; 17 59];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 888;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [5 883; 7 881; 29 859; 31 857; 59 829; 61 827; 227 661; 229 659; 269 619; 271 617];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 4562;\r\ny = twinPrimeGoldbach(n);\r\ny_correct = [13 4549; 43 4519; 139 4423; 433 4129; 643 3919; 1021 3541; 1033 3529; 1093 3469; 1231 3331; 1303 3259; 1873 2689];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 69420;\r\ny = twinPrimeGoldbach(n);\r\nprod_correct = [1179851 1318619 15706811 15844739 18601619 18739379 35896379 36033131 41223779 41360219 101016371 101149259 235769459 235893971 300398771 300519059 320138051 320257019 335772659 335890571 406099979 406213019 488632979 488740019 495999971 496106459 692259779 692350331 716418299 716506691 725655779 725743331 729849251 729936419 765755891 765839699 779228459 779310971 859902059 859976339 861682571 861756659 935069171 935134859 971214011 971275139 981012419 981072251 985122059 985181339 1004250179 1004306819 1006791059 1006847339 1010488379 1010544131 1017121499 1017176291 1033200299 1033252691 1050055379 1050105131 1061479259 1061527139 1076165819 1076211179 1086431459 1086474971 1148968259 1148998139 1163400611 1163426339 1167096779 1167121331 1189892219 1189907651 1192330259 1192344371 1195885811 1195897739 1196587331 1196598779 1197745691 1197756299 1203589451 1203593819 1204004411 1204007939 1204666451 1204667819]';\r\nassert(isequal(prod(y,2),prod_correct))\r\n\r\n%%\r\nn = 777774;\r\ny = twinPrimeGoldbach(n);\r\nprodsum_correct = 10687098646246;\r\nassert(isequal(sum(prod(y,2)),prodsum_correct))\r\n\r\n%%\r\nn = 53942456;\r\ny = twinPrimeGoldbach(n);\r\nans_correct = 4445;\r\nassert(isequal(size(y,1)+find(y==27237733),ans_correct))\r\n\r\n%%\r\nn = 165324896;\r\ny = twinPrimeGoldbach(n);\r\ns = sum(y(:,2)./y(:,1));\r\ns_correct = 3.257362846413793e+05;\r\nassert(abs(s-s_correct)\u003c1e-8)\r\n\r\n%%\r\na = [];\r\nfor n = 2:2:10000\r\n    y = twinPrimeGoldbach(n);\r\n    if isempty(y)\r\n        a(end+1) = n;\r\n    end\r\nend\r\na_correct = [2 4 94 96 98 400 402 404 514 516 518 784 786 788 904 906 908 1114 1116 1118 1144 1146 1148 1264 1266 1268 1354 1356 1358 3244 3246 3248 4204 4206 4208];\r\nassert(isequal(a,a_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-09-24T02:15:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-09-24T02:15:46.000Z","updated_at":"2024-09-24T02:15:56.000Z","published_at":"2024-09-24T02:15:56.000Z","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 Goldbach conjecture says that every positive even integer greater than 2 can be expressed as the sum of two prime numbers in at least one way. For example, 16 is 3+13, 48 is 5+43, and 210 is 19+191. In these examples, the prime numbers are twin primes, or prime numbers that are 2 away from another prime—for example, 3 and 5, 11 and 13, 41 and 43, 17 and 19, and 191 and 193. \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 fact, as far as we know, all but 35 even numbers can be written as the sum of twin primes. This statement can be called the “twin prime Goldbach conjecture.” The exceptions have an interesting pattern, especially if zero is allowed. \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\u003eWrite a function that takes an even 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\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produces all pairs of twin primes that sum 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:t\u003e. The output should be a two-column matrix with the smaller of the pair in the first column and sorted by the first column. For example, the input 16 should produce \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3 13; 5 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e; notice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[11 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[13 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are not included. If the number cannot be written as the sum of twin primes, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\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\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":60331,"title":"Compute the area of a Q","description":"A figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \r\nWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \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: 477.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 238.85px; transform-origin: 407px 238.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; 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: 380.408px 8px; transform-origin: 380.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \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-collapse: preserve; 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: 316.85px 8px; transform-origin: 316.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; 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 166.85px; text-align: left; transform-origin: 384px 166.85px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Qarea(a,c)\r\n  y = a*c;\r\nend","test_suite":"%%\r\na = 1;\r\nc = sqrt(2);\r\ny = Qarea(a,c);\r\ny_correct = 2.121320343559643;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 2;\r\nc = sqrt(5);\r\ny = Qarea(a,c);\r\ny_correct = 5.031152949374527;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 5/2;\r\nc = sqrt(7);\r\ny = Qarea(a,c);\r\ny_correct = 7.011240974321167;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 3;\r\nc = sqrt(8);\r\ny = Qarea(a,c);\r\ny_correct = 8.013876853447540;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 3;\r\nc = sqrt(11);\r\ny = Qarea(a,c);\r\ny_correct = 11.055415967851332;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 4;\r\nc = sqrt(19);\r\ny = Qarea(a,c);\r\ny_correct = 19.070182877990447;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 5;\r\nc = sqrt(23);\r\ny = Qarea(a,c);\r\ny_correct = 23.019991311901052;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = sqrt(27);\r\nc = sqrt(29);\r\ny = Qarea(a,c);\r\ny_correct = 29.018512609609640;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 6;\r\nc = sqrt(31);\r\ny = Qarea(a,c);\r\ny_correct = 31.086684359134285;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = sqrt(43);\r\nc = sqrt(41);\r\ny = Qarea(a,c);\r\ny_correct = 41.011626258563474;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('Qarea.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-18T15:50:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-18T03:49:34.000Z","updated_at":"2026-03-04T13:41:21.000Z","published_at":"2024-05-18T03:49:49.000Z","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\u003eA figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \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\u003eWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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