A281508 Numbers requiring exactly 261 'Reverse and Add' steps to reach a palindrome.

1999290307891606810, 1999290317791606810, 1999290327691606810, 1999290337591606810, 1999290347491606810, 1999290357391606810, 1999290367291606810, 1999290377191606810, 1999290387091606810, 1999290407881606810, 1999290417781606810, 1999290427681606810, 1999290437581606810

Offset: 1

Author

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 24 2017

Keywords

• nonn
• base

Comments

The sequence starts with 1999290307891606810 and continues for another 125 terms (none previously reported, including the first term) each turning into a 119-digit palindrome after 261 steps until the sequence ends with 1999291987030606810. The distance between successive terms in the reported sequence has 9000000 as the greatest common divisor. No further numbers beyond 1999291987030606810 belonging to the same sequence are known, discovered or reported. Moreover, 1999291987030606810 is currently the largest discovered "most delayed palindrome". The sequence was found empirically using computer modeling algorithms.

It is only a conjecture that there are no further terms. - N. J. A. Sloane, Jan 24 2017

Examples

			Each term requires exactly 261 steps to turn into a 119-digit palindrome, the last term of A281509, and is separated by some multiples of 9000000 from the adjacent sequence terms.
		

References

• Popular Computing (Calabasas, CA), The 196 Problem, Vol. 3 (No. 30, Sep 1975).

Links

• Sergei D. Shchebetov, Table of n, a(n) for n = 1..126
• Jason Doucette, World Records
• Yutaka Nishiyama, Numerical Palindromes and the 196 Problem, International Journal of Pure and Applied Mathematics, Volume 80 No. 3 2012, 375-384.
• R. Styer, The Palindromic Conjecture and the Fibonacci Sequence, Villanova University, 1986, 1-11.
• C. W. Trigg, Palindromes by Addition, Mathematics Magazine, 40 (1967), 26-28.
• C. W. Trigg, More on Palindromes by Reversal-Addition, Mathematics Magazine, 45 (1972), 184-186.
• Wikipedia, Lychrel Number
• 196 and Other Lychrel Numbers, 196 and Lychrel Number
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A023109, A033672, A065198, A065199, A065320, A065321, A065322, A065323, A065324, A065325, A065326, A065327, A070743, A072216, A072217, A072218, A281301, A281390, A281506, A281507.