A286481 Numbers which require exactly 260 'Reverse and Add' steps to reach a palindrome.

1003062289999939142, 1003062299899939142, 1003062389989939142, 1003062399889939142, 1003062489979939142, 1003062499879939142, 1003062589969939142, 1003062599869939142, 1003062689959939142, 1003062699859939142, 1003062789949939142, 1003062799849939142, 1003062889939939142, 1003062899839939142, 1003062989929939142, 1003062999829939142

Offset: 1

Author

Andrey S. Shchebetov and Sergei D. Shchebetov, May 12 2017

Keywords

• nonn
• base

Comments

The sequence starts with 1003062289999939142 (the 19-digit number discovered by Vaughn Suite on Mar 19 2006) and continues for another 430079 terms (none previously reported) each turning into a 119-digit palindrome after 260 steps until the sequence ends with 3419399999822603000 (see a-file). No further numbers beyond 3419399999822603000 belonging to the same sequence exist. The sequence was predicted theoretically and found empirically using computer modeling algorithms. For the first 100 terms of the sequence see b-file.

Examples

			a(1) = 1003062289999939142 + 2419399999822603001 = 3422462289822542143
		

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..99
• 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.
• Sergei D. Shchebetov, 430080 terms (zipped file)
• 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, A281508, A281509.

Formula

a(n+1) = a(n) + rev(a(n)).