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A161903 Convert n into a sequence of binary digits, apply one step of the rule 110 cellular automaton, and interpret the results as a binary integer.

%I A161903 #24 Feb 16 2025 08:33:10
%S A161903 0,3,6,7,12,15,14,13,24,27,30,31,28,31,26,25,48,51,54,55,60,63,62,61,
%T A161903 56,59,62,63,52,55,50,49,96,99,102,103,108,111,110,109,120,123,126,
%U A161903 127,124,127,122,121,112,115,118,119,124,127,126,125,104,107,110,111,100,103,98,97,192,195,198,199,204,207,206,205,216,219,222,223,220,223,218,217,240,243,246,247,252,255,254,253,248,251,254,255,244,247,242,241,224,227,230,231,236
%N A161903 Convert n into a sequence of binary digits, apply one step of the rule 110 cellular automaton, and interpret the results as a binary integer.
%C A161903 a(a(a(...1))) (n times) gives A006978(n)
%H A161903 T. D. Noe, <a href="/A161903/b161903.txt">Table of n, a(n) for n = 0..1023</a>
%H A161903 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A161903 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule110.html">Rule 110</a>
%H A161903 Wikipedia, <a href="http://en.wikipedia.org/wiki/Rule_110">Rule 110</a>
%F A161903 a(n) = A057889(A269174(A057889(n))). - _Antti Karttunen_, Jun 02 2018
%e A161903 For n=19, the evolution after one step is
%e A161903 0, 1, 0, 0, 1, 1  (n=19)
%e A161903 1, 1, 0, 1, 1, 1  (a(n)=55)
%e A161903 So a(n)=55.
%t A161903 a[n_] :=
%t A161903 FromDigits[
%t A161903   Drop[Part[CellularAutomaton[110, {IntegerDigits[n, 2], 0}], 1], -1],
%t A161903    2];Table[a[n],{n,0,100}]
%Y A161903 Cf. A006978, A070887, A071049, A180001, A186083, A204371.
%Y A161903 Cf. also A269160, A269174, A269175.
%K A161903 nonn,base
%O A161903 0,2
%A A161903 _Ben Branman_, Jan 30 2011