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#1 2019-05-23 16:27:16
- Anthony Lahmann
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When is n(2n+1) a palindrome?
Last edited by Anthony Lahmann (2019-05-23 16:29:18)
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#2 2019-05-24 11:50:54
- Jaspers
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Re: When is n(2n+1) a palindrome?
If
is a palindrome, when is a palindrome? By looking at this chart, it looks like the only values that work are . The values of are . Is it true that these are the only palindromes of the form , where is a palindrome? If true, prove why. Otherwise, find a counterexample.
Hi Anthony.
I’ve found another one:
Last edited by Jaspers (2019-05-24 14:18:13)
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#3 2019-05-24 15:49:54
- phrontister
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Re: When is n(2n+1) a palindrome?
Hi Anthony & Jaspers;
I found these:
Last edited by phrontister (2019-05-25 03:07:58)
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#4 2019-05-29 15:08:35
- Anthony Lahmann
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Re: When is n(2n+1) a palindrome?
Hi Anthony & Jaspers;
I found these:
The statement "0 is a palindrome" is ambiguous. That's why I excluded it.
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#5 2019-05-29 15:10:14
- Anthony Lahmann
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Re: When is n(2n+1) a palindrome?
Anthony Lahmann wrote:If
is a palindrome, when is a palindrome? By looking at this chart, it looks like the only values that work are . The values of are . Is it true that these are the only palindromes of the form , where is a palindrome? If true, prove why. Otherwise, find a counterexample.Hi Anthony.
I’ve found another one:
Is that the next smallest one?
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#6 2019-05-29 16:26:41
- phrontister
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Re: When is n(2n+1) a palindrome?
Hi Anthony,
A computer program I ran found that 1331 ⇒ 3544453 is the next smallest palindromic pairing of n ⇒ n(2n+1) after your 66 ⇒ 8778.
It gave the following list as the first 12 such pairings:
0 ⇒ 0
1 ⇒ 3
5 ⇒ 55
9 ⇒ 171
66 ⇒ 8778
1331 ⇒ 3544453
123321 ⇒ 30416261403
1332222331 ⇒ 3549632679762369453
13322222331 ⇒ 354963215686512369453
123322223321 ⇒ 30416741529792514761403
133222222331 ⇒ 35496321045754012369453
1233222223321 ⇒ 3041674104186814014761403
Last edited by phrontister (2019-06-06 16:25:07)
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#7 2019-05-29 22:55:56
- phrontister
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- From: The Land of Tomorrow
- Registered: 2009-07-12
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Re: When is n(2n+1) a palindrome?
Hi Anthony,
The statement "0 is a palindrome" is ambiguous. That's why I excluded it.
Wikipedia includes zero as the first palindrome in its list here, as do OEIS here and Wolfram here.
Last edited by phrontister (2019-06-01 12:57:31)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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