A281507 Trajectory of 1186061987030929990 under the "Reverse and Add!" operation.

1186061987030929990, 2185352294922536801, 3271704589845072613, 6434410079699144336, 12768830049399288682, 41457129443403175403, 71914259877895350817, 143719619755790592734, 581014717313707510075, 1151030424627424920260, 1771324671891665221771

Offset: 0

Author

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 23 2017

Keywords

• nonn
• base

Comments

1186061987030929990 is the largest of the first 126 numbers that require exactly 261 steps to turn into a palindrome (see A281506). The sequence reaches a 119-digit palindrome after 261 steps (see b-file). The number was obtained empirically using computer algorithms and was not reported before.

Examples

			a(1) = 1186061987030929990 + 999290307891606811 = 2185352294922536801.
		

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 = 0..261
• 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.

Programs

Magma

k:=1186061987030929990; [n eq 1 select k else Self(n-1) + Seqint(Reverse(Intseq(Self(n-1)))): n in [1..20]]; // Bruno Berselli, Jan 23 2017

Mathematica

NestList[#+IntegerReverse[#]&,1186061987030929990,20] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 17 2019 *)

Formula

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