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#1 2019-05-23 16:27:16

Anthony Lahmann
Member
Registered: 2019-04-25
Posts: 6

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
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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#2 2019-05-24 11:50:54

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

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:

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


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#3 2019-05-24 15:49:54

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,633

Re: When is n(2n+1) a palindrome?

Hi Anthony & Jaspers;

I found these:







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


"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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#4 2019-05-29 15:08:35

Anthony Lahmann
Member
Registered: 2019-04-25
Posts: 6

Re: When is n(2n+1) a palindrome?

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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#5 2019-05-29 15:10:14

Anthony Lahmann
Member
Registered: 2019-04-25
Posts: 6

Re: When is n(2n+1) a palindrome?

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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#6 2019-05-29 16:26:41

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,633

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)


"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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#7 2019-05-29 22:55:56

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,633

Re: When is n(2n+1) a palindrome?

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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