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A352528 The binary expansion of a(n) is obtained by applying the elementary cellular automaton with rule (2*n) mod 256 to the binary expansion of n.

%I A352528 #13 Feb 16 2025 08:34:03
%S A352528 0,1,1,2,0,4,2,6,2,11,5,12,5,12,4,12,0,17,9,26,4,21,14,30,2,19,3,18,9,
%T A352528 25,8,24,0,33,17,50,0,36,19,54,2,35,21,52,7,38,21,52,8,41,9,42,28,61,
%U A352528 31,62,6,39,7,38,19,51,17,48,0,65,33,98,0,68,34,103
%N A352528 The binary expansion of a(n) is obtained by applying the elementary cellular automaton with rule (2*n) mod 256 to the binary expansion of n.
%C A352528 The binary digit of a(n) at place value 2^k is a function of the binary digits of n at place values 2^(k+2), 2^(k+1) and 2^k (and of (2*n) mod 256).
%C A352528 We use even elementary cellular automaton rules, so "000" will always evolve to "0", and the binary expansion of a(n) will have finitely many 1's and will be correctly defined.
%H A352528 Rémy Sigrist, <a href="/A352528/b352528.txt">Table of n, a(n) for n = 0..8192</a>
%H A352528 Rémy Sigrist, <a href="/A352528/a352528.png">Scatterplot of the first 2^20 terms</a>
%H A352528 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A352528 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A352528 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A352528 For n = 13:
%e A352528 - we apply rule 26,
%e A352528 - the binary expansion of 26 being "00011010", we apply the following evolutions:
%e A352528       111 110 101 100 011 010 001 000
%e A352528        0   0   0   1   1   0   1   0
%e A352528 - the binary expansion of 13 (with leading zeros) is   "...0001101",
%e A352528 - the binary digit of a(13) at place value 2^0 is 0 (from     "101"),
%e A352528 - the binary digit of a(13) at place value 2^1 is 0 (from    "110"),
%e A352528 - the binary digit of a(13) at place value 2^2 is 1 (from   "011"),
%e A352528 - the binary digit of a(13) at place value 2^3 is 1 (from  "001"),
%e A352528 - the other binary digits of a(13)            are 0 (from "000"),
%e A352528 - so the binary expansion of a(13) is "1100",
%e A352528 - so a(13) = 12.
%o A352528 (PARI) a(n) = { my (v=0, m=n); for (k=0, oo, if (m==0, return (v), bittest(2*n, m%8), v+=2^k); m\=2) }
%Y A352528 Cf. A269160, A269161, A269173, A269174.
%K A352528 nonn,base
%O A352528 0,4
%A A352528 _Rémy Sigrist_, Mar 19 2022