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A281509 Trajectory of 1999291987030606810 (the largest presently known "most delayed palindrome") under the "Reverse and Add!" operation. 3
1999291987030606810, 2185352294922536801, 3271704589845072613, 6434410079699144336, 12768830049399288682, 41457129443403175403, 71914259877895350817, 143719619755790592734, 581014717313707510075, 1151030424627424920260, 1771324671891665221771, 3542550333873429453542, 5996099577656760005995 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

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!

FORMULA

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

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

EXAMPLE

a(1) = 1999291987030606810 + 186060307891929991 = 2185352294922536801.

CROSSREFS

Cf. A023109, A033672, A065198, A065199, A065320, A065321, A065322, A065323, A065324, A065325, A065326, A065327, A070743, A072216, A072217, A072218, A281301, A281390, A281506, A281507, A281508.

Sequence in context: A229864 A113740 A281508 * A115539 A080129 A272519

Adjacent sequences:  A281506 A281507 A281508 * A281510 A281511 A281512

KEYWORD

nonn,base,less

AUTHOR

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

STATUS

approved

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Last modified September 16 12:41 EDT 2019. Contains 327113 sequences. (Running on oeis4.)