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%I #10 Jun 02 2012 17:13:15
%S 26,37,78,135,360,405,744,837,1488,1581,3024,3213,6048,6237,12192,
%T 12573,24384,24765,48960,49725,97920,98685,196224,197757,392448,
%U 393981,785664,788733,1571328,1574397,3144192,3150333
%N Trajectory of 26 under the Reverse and Add! operation carried out in base 2.
%C 26 is the second-smallest number (after 22) whose base 2 trajectory does not contain a palindrome.
%C lim_{n -> infinity} a(n)/a(n-1) = 2 for n mod 2 = 0.
%C lim_{n -> infinity} a(n)/a(n-1) = 1 for n mod 2 = 1. - Branman
%C In 2001, Brockhaus proved that if the binary Reverse and Add trajectory of an integer contains an integer of one of four specific given forms, then the trajectory never reaches a palindrome. In the case of 26, that would be 3(2^(2k + 1) - 2^k), with k = 3 corresponding to 360. - _Alonso del Arte_, Jun 02 2012
%H Klaus Brockhaus, <a href="/A058042/a058042.txt">On the'Reverse and Add!' algorithm in base 2</a>
%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e In binary, 26 is 11010.
%e a(1) = 37 because 11010 + 01011 = 100101, or 37.
%e a(2) = 78 because 100101 + 101001 = 1001110, or 78.
%t binRA[n_] := If[Reverse[IntegerDigits[n, 2]] == IntegerDigits[n, 2], n, FromDigits[Reverse[IntegerDigits[n, 2]], 2] + n]; NestList[binRA, 26, 100]
%Y Cf. A035522, A061561, A066059, A077076, A077077.
%K nonn,base
%O 0,1
%A _Ben Branman_, Jun 01 2012
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