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A213012 Trajectory of 26 under the Reverse and Add! operation carried out in base 2.

%I A213012 #10 Jun 02 2012 17:13:15
%S A213012 26,37,78,135,360,405,744,837,1488,1581,3024,3213,6048,6237,12192,
%T A213012 12573,24384,24765,48960,49725,97920,98685,196224,197757,392448,
%U A213012 393981,785664,788733,1571328,1574397,3144192,3150333
%N A213012 Trajectory of 26 under the Reverse and Add! operation carried out in base 2.
%C A213012 26 is the second-smallest number (after 22) whose base 2 trajectory does not contain a palindrome.
%C A213012 lim_{n -> infinity} a(n)/a(n-1) = 2 for n mod 2 = 0.
%C A213012 lim_{n -> infinity} a(n)/a(n-1) = 1 for n mod 2 = 1. - Branman
%C A213012 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 A213012 Klaus Brockhaus, <a href="/A058042/a058042.txt">On the'Reverse and Add!' algorithm in base 2</a>
%H A213012 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e A213012 In binary, 26 is 11010.
%e A213012 a(1) = 37 because 11010 + 01011 = 100101, or 37.
%e A213012 a(2) = 78 because 100101 + 101001 = 1001110, or 78.
%t A213012 binRA[n_] := If[Reverse[IntegerDigits[n, 2]] == IntegerDigits[n, 2], n, FromDigits[Reverse[IntegerDigits[n, 2]], 2] + n]; NestList[binRA, 26, 100]
%Y A213012 Cf. A035522, A061561, A066059, A077076, A077077.
%K A213012 nonn,base
%O A213012 0,1
%A A213012 _Ben Branman_, Jun 01 2012