Problem 58013. Find a number m such that 2m and the square of m have the same digit sum

Created by ChrisR

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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: 102px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 51px; transform-origin: 407px 51px; vertical-align: baseline; "><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: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; "><span style="">The number </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="m = 29" style="width: 47.5px; height: 18px;" width="47.5" height="18"></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: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; "><span style=""> has the property that </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="2m = 58" style="width: 55px; height: 18px;" width="55" height="18"></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: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; "><span style=""> and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="m^2 = 841" style="width: 60px; height: 19px;" width="60" height="19"></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: 159.842px 8px; transform-origin: 159.842px 8px; unicode-bidi: normal; "><span style=""> have the same digit sum. It is the seventh number, including zero, in the sequence of numbers with that property. </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: 83.1px 8px; transform-origin: 83.1px 8px; unicode-bidi: normal; "><span style="">Write a function to find the </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: 98.0167px 8px; transform-origin: 98.0167px 8px; unicode-bidi: normal; "><span style="">th term in the sequence, where </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: 53.275px 8px; transform-origin: 53.275px 8px; unicode-bidi: normal; "><span style=""> can be a vector. </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: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; "><span style=""></span></span></div></div></div>

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Last Solution submitted on Aug 29, 2023

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Christian Schröder on 23 Apr 2023

> It is the sixth number, including zero, in the sequence of numbers with that property.

Isn't it the seventh?

Also, out of curiosity, why are you disallowing persistent variables?

ChrisR on 23 Apr 2023

Yes, seventh--corrected, thanks. Bitten by the "off by one bug" again.

Banning persistent is to add the challenge of dealing with large numbers in Cody time. A while ago I found a quicker way to find the digit sums of a lot of numbers, and this problem was another place to exploit that method.

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Problem 58013. Find a number m such that 2m and the square of m have the same digit sum

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Problem 58013. Find a number m such that 2m and the square of m have the same digit sum

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