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A387312 a(n) is the action of "Rule 30" elementary cellular automaton on the binary representation of n if the cells may only expand into the significant bits.

%I A387312 #25 Sep 04 2025 10:52:48
%S A387312 0,3,7,6,14,13,13,12,28,31,27,26,26,25,25,24,56,59,63,62,54,53,53,52,
%T A387312 52,55,51,50,50,49,49,48,112,115,119,118,126,125,125,124,108,111,107,
%U A387312 106,106,105,105,104,104,107,111,110,102,101,101,100,100,103,99,98,98,97,97,96,224,227,231,230,238,237,237,236,252
%N A387312 a(n) is the action of "Rule 30" elementary cellular automaton on the binary representation of n if the cells may only expand into the significant bits.
%C A387312 A269160 allows cells to expand in both directions; its example gives 111 -> 11001 (as opposed to this 111 -> 1100). This sequence does not allow the cells to expand into the least significant bits.
%C A387312 A269160 is a subsequence.
%C A387312 When calculating the LSB edge, the out-of-bounds cell is taken to be 0.
%H A387312 Mia Boudreau, <a href="/A387312/b387312.txt">Table of n, a(n) for n = 0..9999</a>
%H A387312 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30</a>
%H A387312 The Wolfram Atlas of Simple Programs, <a href="https://atlas.wolfram.com/01/01/30/">Rule 30</a>
%F A387312 a(2*n) = A269160(n).
%e A387312 For a(7): 111 -> 1100, so a(7) = 12.
%e A387312 For a(10): 1010 -> 11011, so a(10) = A269160(5) = 27.
%o A387312 (C)
%o A387312 unsigned long long a(unsigned long long n){
%o A387312  unsigned char rule = 30;
%o A387312  unsigned long long x = 0;
%o A387312  int l = sizeof(unsigned long long) * 8;
%o A387312  for(int i = 0; i < l; i++)
%o A387312   x|=((rule>>(((n>>(i+1)&(i<l-1))<<2)|((n>>i&1)<<1)|(n>>(i-1)&(i>0))))&1)<<i;
%o A387312  return x;
%o A387312 }
%Y A387312 Cf. A269160.
%K A387312 nonn,new
%O A387312 0,2
%A A387312 _Mia Boudreau_, Aug 25 2025