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A281301 Trajectory of 1000004999700144385 under the "Reverse and Add!" operation.

%I A281301 #59 Dec 24 2021 13:33:13
%S A281301 1000004999700144385,6834415079694144386,13668830049399288772,
%T A281301 41457129443403175403,71914259877895350817,143719619755790592734,
%U A281301 581014717313707510075,1151030424627424920260,1771324671891665221771,3542550333873429453542,5996099577656760005995
%N A281301 Trajectory of 1000004999700144385 under the "Reverse and Add!" operation.
%C A281301 1000004999700144385 is the largest of the first 225 numbers that require exactly 259 steps to turn into a palindrome (see A281390). The sequence reaches a 119-digit palindrome after 259 steps (see b-file). The number was obtained empirically using computer algorithms and was not reported before.
%C A281301 Row 1000004999700144385 of the array in A243238. - _Felix Fröhlich_, Jan 21 2017
%D A281301 Popular Computing (Calabasas, CA), The 196 Problem, Vol. 3 (No. 30, Sep 1975).
%H A281301 Sergei D. Shchebetov, <a href="/A281301/b281301.txt">Table of n, a(n) for n = 0..259</a>
%H A281301 Jason Doucette, <a href="http://jasondoucette.com/worldrecords.html">World Records</a>
%H A281301 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 A281301 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 A281301 C. W. Trigg, <a href="http://www.jstor.org/stable/2689178">Palindromes by Addition</a>, Mathematics Magazine, 40 (1967), 26-28.
%H A281301 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 A281301 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lychrel_number">Lychrel Number</a>
%H A281301 196 and Other Lychrel Numbers, <a href="http://www.p196.org/">196 and Lychrel Number</a>
%H A281301 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%F A281301 a(n+1) = a(n) + rev(a(n)).
%e A281301 a(1) = 1000004999700144385 + 5834410079994000001 = 6834415079694144386.
%t A281301 NestList[#+IntegerReverse[#]&,1000004999700144385,10] (* _Harvey P. Dale_, Dec 24 2021 *)
%o A281301 (PARI) terms(n) = my(x=1000004999700144385, i=0); while(1, print1(x, ", "); x=x+eval(concat(Vecrev(Str(x)))); i++; if(i==n, break))
%o A281301 /* Print initial 9 terms as follows: */
%o A281301 terms(9) \\ _Felix Fröhlich_, Jan 21 2017
%Y A281301 Cf. A023109, A033672, A065198, A065199, A065320, A065321, A065322, A065323, A065324, A065325, A065326, A065327, A070743, A072216, A072217, A072218, A243238, A281390.
%K A281301 nonn,base
%O A281301 0,1
%A A281301 Andrey S. Shchebetov and _Sergei D. Shchebetov_, Jan 21 2017
%E A281301 a(9)-a(10) from _Felix Fröhlich_, Jan 21 2017