Problem 52462. Easy Sequences 1: Find the index of an element

Created by Ramon Villamangca

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{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The nth element of a series </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A</w:t></w:r></w:customXml><w:r><w:t> is defined by: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A(n) = \\displaystyle\\sum\\limits_{k=1}^n (k\\cdot(-1)^{k^3+1})</w:t></w:r></w:customXml><w:r><w:t>. Obviously, the first element </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A(1) = 1</w:t></w:r></w:customXml><w:r><w:t>. Given the nth element </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A(n)</w:t></w:r></w:customXml><w:r><w:t>, find the value of the corresponding index </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div 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; "><div style="block-size: 66px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 33px; transform-origin: 407px 33px; vertical-align: baseline; "><div 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: 384px 33px; text-align: left; transform-origin: 384px 33px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; 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: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; "><span style="">The nth element of a series </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">A</span><span style="block-size: auto; display: inline; margin-block-end: 0px; 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; "><span style=""> is defined by: </span></span><span style="vertical-align:-17px"><img src="data:image/png;base64,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" style="width: 155.5px; height: 45px;" width="155.5" height="45"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; 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: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; "><span style="">. Obviously, the first element </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 59px; height: 18.5px;" width="59" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; 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; "><span style="">. Given the nth element </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 33px; height: 18.5px;" width="33" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; 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: 134.5px 8px; transform-origin: 134.5px 8px; unicode-bidi: normal; "><span style="">, find the value of the corresponding index </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><span style="block-size: auto; display: inline; margin-block-end: 0px; 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; "><span style="">.</span></span></div></div></div>

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183 Solutions
32 Solvers

Last Solution submitted on Sep 11, 2022

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7 Comments

Show 4 older comments

Dyuman Joshi on 10 Aug 2021

@Ramon, if you are submitting a question on Cody for everybody to solve, it is recommended you put atleast 3 test suites, mostly so that it encourages people to learn and not hard code solutions.

Ramon Villamangca on 11 Aug 2021

Thanks, @Dyuman. There are now 4 test suites.

Dyuman Joshi on 11 Aug 2021

@Ramon, Wonderful!

David Hill on 12 Aug 2021

-a+(1-(-1)^(n+1))/2 will be negative in the 4th test. I believe it should be: index(a-(1-(-1)^(n+1))/2).

Rahul Gulia on 24 Sep 2021

This works fine in my MATLAB software. But not here.
Any comments, please?

function n = index(a)
for idx = 1:1000
b = idx*((-1)^(idx^3+1));
if b==a
break
else
continue
end
end
n=idx;
end

Dyuman Joshi on 24 Sep 2021

Because you are not doing what the question is asking

Asif Newaz on 21 Aug 2022

I think the last test case is wrong

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Problem 52462. Easy Sequences 1: Find the index of an element

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Problem 52462. Easy Sequences 1: Find the index of an element

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