A281509 Trajectory of 1999291987030606810 (the largest presently known "most delayed palindrome") under the "Reverse and Add!" operation.

1999291987030606810, 2185352294922536801, 3271704589845072613, 6434410079699144336, 12768830049399288682, 41457129443403175403, 71914259877895350817, 143719619755790592734, 581014717313707510075, 1151030424627424920260, 1771324671891665221771, 3542550333873429453542, 5996099577656760005995

Offset: 0

Author

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

Keywords

• nonn
• base
• less

Comments

1999291987030606810 is the largest of the 126 presently known numbers that require exactly 261 steps to turn into a palindrome (see A281508). It is also the largest discovered "most delayed palindrome". 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) = 1999291987030606810 + 186060307891929991 = 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, A281507, A281508.

Formula

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

a(n) = A281507(n) for n>0. - R. J. Mathar, Jan 27 2017