Problem 46003. Compute Khinchin's constant

Created by ChrisR

Solve Later

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<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,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" 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>

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Last Solution submitted on Dec 01, 2021

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Dyuman Joshi on 4 Jan 2022

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

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Problem 46003. Compute Khinchin's constant

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Problem 46003. Compute Khinchin's constant

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