[seqfan] Re: An infinite palindrome

[Veikko Pohjola]

Hi,

Hopefully the following helps to say something about the argument.

Consider the roots in the range n = -10^2...10^2. There are 19 roots:
-90, -87, -84, -65, -62, -43, -40, -21, -18, 1, 4, 23, 26, 45, 48, 67, 70, 89, 92.
The first differences are:
3, (3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3)
where the fraction within parentheses with length 17 is the longest palindrome. Its center of symmetry (3) is between the roots 1 and 4.

Having made calculations up to n = -10^7...10^7, it appears that longer and longer palindromes form. Interestingly, the center of symmetry moves as the range varies. Within this range there are 2,048,312 roots: -9,999,990, ..., -7410, -7407, ..., 9,985,173.
The longest palindrome has the length of 2,046,765 and its center of symmetry (3) is between the roots -7410 and -7407.

Veikko


> Dear seqfans,
> 
> How about the following argument ? 
> The first differences of the roots of Floor[Tan[n]] == 1, where n = -oo ... + oo, is a palindrome.
> 
> Cheers,
> Veikko
> 
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