Problem 56428. Easy Sequences 79: Trailing Zeros of Fibonorial Numbers at any Base

Created by Ramon Villamangca

Solve Later

{"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 </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Fibonorial\"><w:r><w:rPr><w:b/></w:rPr><w:t>fibonorial </w:t></w:r></w:hyperlink><w:r><w:t>of an integer </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> is defined as follows:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\Phi(n)=\\prod_{i=1}^n F_i</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>where: </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>F_i</w:t></w:r></w:customXml><w:r><w:t> is the </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>i</w:t></w:r></w:customXml><w:r><w:t>-th </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Fibonacci_number\"><w:r><w:t>Fibonacci number </w:t></w:r></w:hyperlink><w:r><w:t>(</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>F_1=F_2=1</w:t></w:r></w:customXml><w:r><w:t> and </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>F_i=F_{i-1}+F_{i-2}</w:t></w:r></w:customXml><w:r><w:t> for </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>i&gt;2</w:t></w:r></w:customXml><w:r><w:t>).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>In other words, the fibonorial of </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:r><w:rPr><w:b/></w:rPr><w:t> </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>\\Phi(n)</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, is the product of all Fibonacci numbers from </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>F_1</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> to </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>F_n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given an integer </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> and a number base </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>b</w:t></w:r></w:customXml><w:r><w:t>, write a function that calculates the number of trailing zeros of the fibonorial of </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> when written in base-</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>b</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, for </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=10</w:t></w:r></w:customXml><w:r><w:t> and </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>b=4\n</w:t></w:r></w:customXml><w:r><w:t>, the function should return </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>2</w:t></w:r></w:customXml><w:r><w:t>, because:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ >> dec2base(prod([1 1 2 3 5 8 13 21 34 55]),4)\n >> '13103120230200']]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For </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=10</w:t></w:r></w:customXml><w:r><w:t> and </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>b=13</w:t></w:r></w:customXml><w:r><w:t>, the function should return </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>1</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ >> dec2base(prod([1 1 2 3 5 8 13 21 34 55]),13)\n >> '1C4CB080']]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>--------------------</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Hint:</w:t></w:r><w:r><w:t> As a practice, you may want to solve first, the previous problem: </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/56418-easy-sequences-78-trailing-zeros-of-factorial-numbers-at-any-base\"><w:r><w:t>Easy Sequences 78: Trailing Zeros of Factorial Numbers at any Base</w:t></w:r></w:hyperlink><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: 432.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 216.367px; transform-origin: 407px 216.367px; vertical-align: baseline; "><div 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; "><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: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; ">The <a target='_blank' href = "https://en.wikipedia.org/wiki/Fibonorial">fibonorial </a><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: 42px 8px; transform-origin: 42px 8px; unicode-bidi: normal; ">of an integer n<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: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; "> is defined as follows:</div><div style="block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><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: 40px 8px; transform-origin: 40px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 86px; height: 45px;" width="86" height="45"></div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><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: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; ">where: <img src="data:image/png;base64,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" style="width: 15px; height: 20px;" width="15" height="20"><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: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; "> is the i<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: 10.5px 8px; transform-origin: 10.5px 8px; unicode-bidi: normal; ">-th <a target='_blank' href = "https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci number </a><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: 2.5px 8px; transform-origin: 2.5px 8px; unicode-bidi: normal; ">(<img src="data:image/png;base64,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" style="width: 76px; height: 20px;" width="76" height="20"><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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" style="width: 100.5px; height: 20px;" width="100.5" height="20"><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: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; "> for <img src="data:image/png;base64,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" style="width: 33.5px; height: 18px;" width="33.5" height="18"><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: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; ">).</div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><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: 113px 8px; transform-origin: 113px 8px; unicode-bidi: normal; ">In other words, the fibonorial of n<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="block-size: auto; display: inline; margin-block-end: 0px; 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; "> <img src="data:image/png;base64,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" style="width: 33.5px; height: 18.5px;" width="33.5" height="18.5"><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: 161px 8px; transform-origin: 161px 8px; unicode-bidi: normal; ">, is the product of all Fibonacci numbers from <img src="data:image/png;base64,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" style="width: 17px; height: 20px;" width="17" height="20"><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: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; "> to <img src="data:image/png;base64,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" style="width: 17px; height: 20px;" width="17" height="20"><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; ">.</div><div 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; "><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: 54.5px 8px; transform-origin: 54.5px 8px; unicode-bidi: normal; ">Given an integer n<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: 65.5px 8px; transform-origin: 65.5px 8px; unicode-bidi: normal; "> and a number base b<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: 248px 8px; transform-origin: 248px 8px; unicode-bidi: normal; ">, write a function that calculates the number of trailing zeros of the fibonorial of n<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: 0.25px 8px; transform-origin: 0.25px 8px; unicode-bidi: normal; "> when written in base-b<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; ">.</div><div 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; "><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: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; ">For example, for <img src="data:image/png;base64,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" style="width: 44px; height: 18px;" width="44" height="18"><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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" style="width: 36.5px; height: 18px;" width="36.5" height="18"><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: 87px 8px; transform-origin: 87px 8px; unicode-bidi: normal; ">, the function should return 2<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: 33px 8px; transform-origin: 33px 8px; unicode-bidi: normal; ">, because:</div><div style="background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 192px 8.5px; tab-size: 4; transform-origin: 192px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "> &gt;&gt; dec2base(prod([1 1 2 3 5 8 13 21 34 55]),4)</div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "> &gt;&gt; <span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 64px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 64px 8.5px; ">'13103120230200'</div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; 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: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; ">For <img src="data:image/png;base64,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" style="width: 44px; height: 18px;" width="44" height="18"><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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" style="width: 44px; height: 18px;" width="44" height="18"><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: 87px 8px; transform-origin: 87px 8px; unicode-bidi: normal; ">, the function should return 1<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; ">.</div><div style="background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 196px 8.5px; tab-size: 4; transform-origin: 196px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "> &gt;&gt; dec2base(prod([1 1 2 3 5 8 13 21 34 55]),13)</div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "> &gt;&gt; <span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 40px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 40px 8.5px; ">'1C4CB080'</div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; 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: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; ">--------------------</div><div 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; "><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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; ">Hint:<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: 204.5px 8px; transform-origin: 204.5px 8px; unicode-bidi: normal; "> As a practice, you may want to solve first, the previous problem: <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/56418-easy-sequences-78-trailing-zeros-of-factorial-numbers-at-any-base">Easy Sequences 78: Trailing Zeros of Factorial Numbers at any Base</a><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; ">.</div></div></div>

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Last Solution submitted on Feb 19, 2023

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GeeTwo on 21 Dec 2022

Note that in addition to global, persistent, java and BigInteger; for, if, case, and switch are forbidden.
Only needs scalar inputs - test cases do arrayfun()s.

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Solution 10184167

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1 Comment

GeeTwo on 22 Dec 2022

No lookups, no strings. I did kludge a recursion hack against variable scope because I needed sequential iteration.

Solution 9662133

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Ramon Villamangca on 1 Nov 2022

Hi, there is also a solution that does not rely in hardcoded lookup array.

David Hill on 1 Nov 2022

Are you saying there is an easy way to generate the lookup values or that there is a method that doesn't need those values?

Ramon Villamangca on 1 Nov 2022

you can make a lookup array if you like. but it is not necessary to hardcode any values. when i made this problem i didn't see that the test requires only a few primes will be used. which makes it even more easier to create an array of prime entry points without precomputing. in fact, there is actually no reason to make a lookup list.

Ramon Villamangca on 1 Nov 2022

you can learn about prime entry points here: https://r-knott.surrey.ac.uk/Fibonacci/fibCalcX.html

GeeTwo on 17 Dec 2022

Found on oeis A001177, prime p divides exactly one of a(p-1:p+1). This means that the entry point is a factor of one of those three. Probably sufficient here is that it is never larger than p+1.

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Problem 56428. Easy Sequences 79: Trailing Zeros of Fibonorial Numbers at any Base

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Problem 56428. Easy Sequences 79: Trailing Zeros of Fibonorial Numbers at any Base

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