Problem 46003. Compute Khinchin's constant

Created by ChrisR

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>Khinchin's constant </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"K_0\"/></w:customXmlPr><w:r><w:t>K_0</w:t></w:r></w:customXml><w:r><w:t> = 2.684542001... (also written \"Khintchine's constant\") has the amazing property that it is the limiting value of the geometric mean of the partial quotients from a continued fraction expansion of almost all numbers. In other words, if a number </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>x</w:t></w:r></w:customXml><w:r><w:t> is expanded as</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:attr w:name=\"altTextString\" w:val=\"Continued fraction expansion of x\"/></w:customXmlPr><w:r><w:t>x = a_0+\\frac{1}{a_1+\\frac{1}{a_2+\\frac{1}{a_3 + \\frac{1}{\\ddots}}</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>then as </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"n approaches infinity\"/></w:customXmlPr><w:r><w:t>n\\to\\infty</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>       </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"K_0 is the nth root of the product of a_1 through a_n\"/></w:customXmlPr><w:r><w:t>K_0 = (a_1a_2a_3\\ldots a_n)^{1/n}</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>More information is available at</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Khinchin%27s_constant\"><w:r><w:t>Wikipedia</w:t></w:r></w:hyperlink><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://mathworld.wolfram.com/KhinchinsConstant.html\"><w:r><w:t>Wolfram MathWorld</w:t></w:r></w:hyperlink><w:r><w:t>, the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://oeis.org/A002210\"><w:r><w:t>Online Encyclopedia of Integer Sequences</w:t></w:r></w:hyperlink><w:r><w:t>, and</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.youtube.com/watch?v=VDD6FDhKCYA\"><w:r><w:t>Numberphile</w:t></w:r></w:hyperlink><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>Compute Khinchin's constant. The test suite will check for a difference of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"10^{-12}\"/></w:customXmlPr><w:r><w:t>10^{-12}</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: 298.833px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 149.417px; transform-origin: 407px 149.417px; vertical-align: baseline; "><div style="block-size: 63.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.6333px; text-align: left; transform-origin: 384px 31.6333px; 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: 62.0167px 7.91667px; transform-origin: 62.0167px 7.91667px; unicode-bidi: normal; "><span style="">Khinchin's constant </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="K_0" style="width: 18px; height: 20px;" width="18" height="20"></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: 312.983px 7.91667px; transform-origin: 312.983px 7.91667px; unicode-bidi: normal; "><span style=""> = 2.684542001... (also written "Khintchine's constant") has the amazing property that it is the limiting value of the geometric mean of the partial quotients from a continued fraction expansion of almost all numbers. In other words, if a number </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);">x</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: 49.0167px 7.91667px; transform-origin: 49.0167px 7.91667px; unicode-bidi: normal; "><span style=""> is expanded as</span></span></div><div style="block-size: 85.3333px; 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 42.6667px; text-align: left; transform-origin: 384px 42.6667px; 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: 13.6px 7.91667px; transform-origin: 13.6px 7.91667px; unicode-bidi: normal; "><span style="">       </span></span><span style="vertical-align:-69px"><img src="data:image/png;base64,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" alt="Continued fraction expansion of x" style="width: 160.5px; height: 85.5px;" width="160.5" height="85.5"></span></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: 24.9px 7.91667px; transform-origin: 24.9px 7.91667px; unicode-bidi: normal; "><span style="">then as </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="n approaches infinity" style="width: 46.5px; height: 18px;" width="46.5" height="18"></span></div><div style="block-size: 21.25px; 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 10.6333px; text-align: left; transform-origin: 384px 10.6333px; 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: 13.6px 7.91667px; transform-origin: 13.6px 7.91667px; unicode-bidi: normal; "><span style="">       </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQsAAAAqCAYAAACk0n51AAAGpUlEQVR4nO2d65HiMBCEOwcyIAEScAQbARmQARmQAjEQwuZACsRACns/5C43Or1s+c18Va6rBWPJstSaGY18gGEYhmEYhmEYhmEYxiScAVyXroRhGPNyAHBp/y3lF8BxmuoYhrFGzgDeAP5QLhZHOLEwDONLuAH4gROKPmJxhRMZYyFO6GcGGoZywHC3oK9YvAaWY4zAGcB96UoYm+YA4IFhM34fsThihr7awJk9L3SV43GHC7CQK5xPpOe82s/3NvuaUBhj8kR/wegjFle4sRyiactu5O/U+VnUR/rDp0jEzrtjn5HXHzgR3JsAGstxgOtTpx6/6SMWIRfkCCcKvM4Jbsw+2r+fPerygYpAbKCc0EVoY2KydY5w9zhYdQ0jQt9JqFQsGsSt4AM6Ybi3deC1B8c47vi0GHwoFC/seyDdYctPxnT8wrn9JZSKxR3xMUkj4CnlNu1npfX4D41Z+L7Vuf187wkfR7j73LMYGsvCsVQyjkrFImUh0AjQc+ia/AR/kYGDhAdvhJHcP+wziOlzhy0/GdPzRllKdolY5NK7aQSoAcBFikHj+SIVe7YXObUFvfE9iR5v2AqIMT0PlE1KJWKRsvZpBPhl0UsYBK0H+jEUjyf6RW+3DP24IcJ4hmv8Z/vvvf3sCSdAY1hkDdxzYhkPODOSs8QYrtMcZaydOdqAbkDOFcmJRS69my6PxiYYw7hiYMYnVzioQhSKueMTHLC1x5CVGj7APp3hhE4Q1P9TS602WKquoG4qOkkZtYI0RxlrZ842YD9PxQx0LMQm7NxgZ7xC+zT7+QMDApzaGP4xKABSwZJiwYYt7QxcHQots+p91CwxH+DEKHYdlvFYeRlrZ+42YP+IxRp+0M38PEKTWG4iuuD/+zm01xs0tjVpg8s6Gr/4FmhmlqD5JqFGL5kVcmgHjs0AtYI0RxlrZ4k2YO7D4KVLzJTe7aPp21zxULekj09zhGvQqlTShSgVC2bipWYaCjCDxTHOiIsJTeJYEo8KUshdZEpv6lnUlnGSMua2Qseitg2GUuuizr7DlArHg51KrY134bWu6EzyI9xA2ZLpWioWfvpsCM5UMeVv5JycZRKbzWgB+oLEmfIlZVDY9LyaMgB3b2+4duPksqXnDdS3QQ21YjH7Er+mePvBG03Syq0J8zra4Fy2qTG15qRELNTqig0M7YAh5b+gS/uNiQXrEpvttB6+IP3i8zmoy3T1zhtaxhmf4qPW1pZWz2raoJaaa6bSuydD4xN+5z/Ld7nAHzuKb6ZxpaDUfFsywElzNIW2ScwEVLcudd88zxcLTZCLdQi1brQetOh8dCm8tgxEflOVFbgAtW1QQy7AuUrUeggNMO34sQblakrIXeEKQ+ngXcPSaWpm1P0zISFQSy0XHI6JRU6QuNEtJOLHSP3ZrqxTTRkxbih3WdfAFG1QSk1OzyL4Kd6pTpY6h40eGhwcgFvIiuRAT82MKp5+52HOBQWY9/yDcLvFxEJnM/87xiP4W822LVmzp0s4dhl0Q/oGtU8oszrHPg8Ypw34Nwc9t4TnRICW3mZcNlXW1LZZHSChgIxG/vt8tzYY7E2ZhmpZ6INmarxaFmd0WZyhti2xLNRCYge+4DOAyrJTHc+3msYso2m/e6HfTJkarFOeR2rb4IpuYrigy+Jl7k1KtBgc3gwqAqnIqj6EkOm0F7EAujTfGGppcTMQH3zjff9EOgs2Jhb+0vUNnYnPTq3PrWRGf+Ez0DxWGUweUne21LoocXGnOI+M0QaayMX2ZT1SYrGZPUhUQN/P998TeEbXeKlz9yQWJduHL+gGB18pqLt0ufku9xaxmFgAn0urvJbO6gzGPpAfnKzvlGUAndVVOgg4U+f2H419nlLTBrREX/i0uHP9nRPKZlyQMdGXa/hoHvpW8GfhqUiJxVgwjjLXng4O1m9A3RhOCiUvlfnqlyvFtsEC/VdD1kCDfsu9Q5laLOh7z5lJ+4vvGQghSyq3fMyVwz2/QCpLKs9iiybXDdNbQ1OKxaG9fkgoplyue2JjuQMVhPp8LrGPgdOvJpXBuYlAToAHpn2wU4mFRvN9uG+nFn2tPJnLIlsD7NvqcjGGQZH2+/0t8NnXwmBog8916q2+A+GA7iU2U1x7qrek64uMQscYg1kD3cwz+MX2LMihMF6hwst4RcgVs/+DJgCTUq7YT8cZ+92julNTd2yOUUbo2nqMJXz6nC/Yz7MuhUvG/jMLvT/iGPjMMAzDMAzDMAzDMAzDMAzDMAzDMAzDWC//AEaigcAXd+7JAAAAAElFTkSuQmCC" alt="K_0 is the nth root of the product of a_1 through a_n" style="width: 133.5px; height: 21px;" width="133.5" height="21"></span></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: 96.8667px 7.91667px; transform-origin: 96.8667px 7.91667px; unicode-bidi: normal; "><span style="">More information is available at</span></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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Khinchin%27s_constant"><span style=""><span style="">Wikipedia</span></span></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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style="">,</span></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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://mathworld.wolfram.com/KhinchinsConstant.html"><span style=""><span style="">Wolfram MathWorld</span></span></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: 13.6167px 7.91667px; transform-origin: 13.6167px 7.91667px; unicode-bidi: normal; "><span style="">, the</span></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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://oeis.org/A002210"><span style=""><span style="">Online Encyclopedia of Integer Sequences</span></span></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: 15.5667px 7.91667px; transform-origin: 15.5667px 7.91667px; unicode-bidi: normal; "><span style="">, and</span></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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://www.youtube.com/watch?v=VDD6FDhKCYA"><span style=""><span style="perspective-origin: 39.7px 7.91667px; transform-origin: 39.7px 7.91667px; ">Numberphile</span></span></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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style="">.</span></span></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: 226.417px 7.91667px; transform-origin: 226.417px 7.91667px; unicode-bidi: normal; "><span style="">Compute Khinchin's constant. The test suite will check for a difference of </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="10^{-12}" style="width: 35px; height: 19.5px;" width="35" height="19.5"></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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

Solve

Solution Stats

42 Solutions
11 Solvers

Last Solution submitted on Dec 01, 2021

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Dyuman Joshi on 4 Jan 2022 at 10:08

This is people finding a way to go around the test case

Problem Recent Solvers11

Problem Tags

number theory numbers

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 46003. Compute Khinchin's constant

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers11

Suggested Problems

More from this Author136

Problem Tags

Community Treasure Hunt

Problem 46003. Compute Khinchin's constant

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers11

Suggested Problems

More from this Author136

Problem Tags

Community Treasure Hunt

Players