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%I #63 May 14 2017 12:32:03
%S 1000000079994144385,1000000089894144385,1000000099794144385,
%T 1000000179984144385,1000000189884144385,1000000199784144385,
%U 1000000279974144385,1000000289874144385,1000000299774144385,1000000379964144385,1000000389864144385,1000000399764144385
%N Numbers which require exactly 259 'Reverse and Add' steps to reach a palindrome.
%C The sequence starts with 1000000079994144385 (the 19-digit 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 119-digit 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.
%C The sequence was extended to 1620000 terms in total and currently ends with 6834414999700000000 (see a-file). 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
%D Popular Computing (Calabasas, CA), The 196 Problem, Vol. 3 (No. 30, Sep 1975).
%H Sergei D. Shchebetov, <a href="/A281390/b281390.txt">Table of n, a(n) for n = 1..225</a>
%H Jason Doucette, <a href="http://jasondoucette.com/worldrecords.html">World Records</a>
%H Yutaka Nishiyama, <a href="http://www.ijpam.eu/contents/2012-80-3/9/index.html">Numerical Palindromes and the 196 Problem</a>, International Journal of Pure and Applied Mathematics, Volume 80 No. 3 2012, 375-384.
%H Sergei D. Shchebetov, <a href="/A281390/a281390-1620000.zip">1620000 terms (zipped file)</a>
%H R. Styer, <a href="http://www41.homepage.villanova.edu/robert.styer/PalindromePaper1986.pdf">The Palindromic Conjecture and the Fibonacci Sequence</a>, Villanova University, 1986, 1-11.
%H C. W. Trigg, <a href="http://www.jstor.org/stable/2689178">Palindromes by Addition</a>, Mathematics Magazine, 40 (1967), 26-28.
%H C. W. Trigg, <a href="http://www.jstor.org/stable/2688651">More on Palindromes by Reversal-Addition</a>, Mathematics Magazine, 45 (1972), 184-186.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lychrel_number">Lychrel Number</a>
%H 196 and Other Lychrel Numbers, <a href="http://www.p196.org/">196 and Lychrel Number</a>
%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e Each term requires exactly 259 steps to turn into a 119-digit palindrome, the last term of A281301, and is separated by some multiples of 9000000 from the adjacent sequence terms.
%Y Cf. A023109, A033672, A065198, A065199, A065320, A065321, A065322, A065323, A065324, A065325, A065326, A065327, A070743, A072216, A072217, A072218, A281301.
%Y See also A286481.
%K nonn,base
%O 1,1
%A Andrey S. Shchebetov and _Sergei D. Shchebetov_, Jan 21 2017
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