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**Anthony Lahmann****Member**- Registered: 2019-04-25
- Posts: 9

If is a palindrome, when is a palindrome? By looking at this chart, it looks like the only values that work are and . The values of are and . Is it true that these are the only palindromes of the form , where is a palindrome? If true, prove why. Otherwise, find a counterexample.

*Last edited by Anthony Lahmann (2019-05-23 16:29:18)*

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**Jaspers****Member**- Registered: 2019-05-24
- Posts: 54

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:

*Last edited by Jaspers (2019-05-24 14:18:13)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,650

Hi Anthony & Jaspers;

I found these:

*Last edited by phrontister (2019-05-25 03:07:58)*

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**Anthony Lahmann****Member**- Registered: 2019-04-25
- Posts: 9

phrontister wrote:

Hi Anthony & Jaspers;

I found these:

The statement "0 is a palindrome" is ambiguous. That's why I excluded it.

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**Anthony Lahmann****Member**- Registered: 2019-04-25
- Posts: 9

Jaspers wrote:

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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,650

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)*

"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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,650

Hi Anthony,

Anthony Lahmann wrote:

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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