

A281390


Numbers which require exactly 259 'Reverse and Add' steps to reach a palindrome.


8



1000000079994144385, 1000000089894144385, 1000000099794144385, 1000000179984144385, 1000000189884144385, 1000000199784144385, 1000000279974144385, 1000000289874144385, 1000000299774144385, 1000000379964144385, 1000000389864144385, 1000000399764144385
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OFFSET

1,1


COMMENTS

The sequence starts with 1000000079994144385 (the 19digit number discovered by Vaughn Suite on Jul 26 2005 and rediscovered by Jason Doucette on Nov 28 2005) and continues for another 224 terms (none previously reported) each turning into a 119digit palindrome after 259 steps until the sequence ends with 1000004999700144385. The distance between successive terms in the reported sequence has 9000000 as the greatest common divisor. No further numbers beyond 1000004999700144385 belonging to the same sequence are known, discovered or reported. The sequence was found empirically using computer modeling algorithms.
The sequence was extended to 1620000 terms in total and currently ends with 6834414999700000000 (see afile). The sequence is complete  no further numbers beyond 6834414999700000000 belonging to the same sequence exist. The sequence was predicted theoretically and found empirically using computer modeling algorithms.  Sergei D. Shchebetov, May 12 2017


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..225
Jason Doucette, World Records
Yutaka Nishiyama, Numerical Palindromes and the 196 Problem, International Journal of Pure and Applied Mathematics, Volume 80 No. 3 2012, 375384.
Sergei D. Shchebetov, 1620000 terms (zipped file)
R. Styer, The Palindromic Conjecture and the Fibonacci Sequence, Villanova University, 1986, 111.
C. W. Trigg, Palindromes by Addition, Mathematics Magazine, 40 (1967), 2628.
C. W. Trigg, More on Palindromes by ReversalAddition, Mathematics Magazine, 45 (1972), 184186.
Wikipedia, Lychrel Number
196 and Other Lychrel Numbers, 196 and Lychrel Number
Index entries for sequences related to Reverse and Add!


EXAMPLE

Each term requires exactly 259 steps to turn into a 119digit palindrome, the last term of A281301, and is separated by some multiples of 9000000 from the adjacent sequence terms.


CROSSREFS

Cf. A023109, A033672, A065198, A065199, A065320, A065321, A065322, A065323, A065324, A065325, A065326, A065327, A070743, A072216, A072217, A072218, A281301.
See also A286481.
Sequence in context: A172546 A256312 A173445 * A281301 A286481 A168334
Adjacent sequences: A281387 A281388 A281389 * A281391 A281392 A281393


KEYWORD

nonn,base


AUTHOR

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 21 2017


STATUS

approved



