cp's OEIS Frontend

A051023 Middle column of rule-30 1-D cellular automaton, from a lone 1 cell.

%I A051023 #73 Feb 16 2025 08:32:41
%S A051023 1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,1,0,1,1,1,0,0,1,
%T A051023 1,1,0,1,0,1,0,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,1,1,1,1,1,
%U A051023 0,0,0,0,1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0,1,0,1,1,0,0,0,1
%N A051023 Middle column of rule-30 1-D cellular automaton, from a lone 1 cell.
%C A051023 A092539(n) gives the value of prefix of length n+1, seen as a binary number. - _Reinhard Zumkeller_, Jun 08 2013
%C A051023 Also middle column of rule 86 1-D cellular automaton, from a lone 1 cell, as rule 86 is the mirror image of rule 30. - _Antti Karttunen_, Oct 03 2019
%H A051023 Antti Karttunen, <a href="/A051023/b051023.txt">Table of n, a(n) for n = 0..100000</a> (terms 0..10000 from Reinhard Zumkeller)
%H A051023 Pedro Hecht, <a href="https://ia.cr/2021/672">PQC: R-Propping a Chaotic Cellular Automata</a>, Univ. of Buenos Aires (Argentina, 2021).
%H A051023 Erica Jen, <a href="https://doi.org/10.1007/BF01010579">Global properties of cellular automata</a>, Journal of Statistical Physics 43 (1986), pp 219-242.
%H A051023 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton.</a>
%H A051023 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30</a>
%H A051023 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RandomNumber.html">Random Number</a>
%H A051023 Xiangdong Wen, <a href="https://datarepository.wolframcloud.com/resources/A-Billion-Bits-of-the-Center-Column-of-the-Rule-30-Cellular-Automaton">A Billion Bits of the Center Column of the Rule 30 Cellular Automaton</a>, 2019
%H A051023 Stephen Wolfram, <a href="https://blog.wolfram.com/2019/10/01/announcing-the-rule-30-prizes/">Announcing the Rule 30 Prizes</a>, 2019
%H A051023 Stephen Wolfram, <a href="https://datarepository.wolframcloud.com/resources/A-Million-Bits-of-the-Center-Column-of-the-Rule-30-Cellular-Automaton">A Million Bits of the Center Column of the Rule 30 Cellular Automaton</a>, 2017
%H A051023 Wolfram Mathematica, <a href="https://library.wolfram.com/infocenter/Demos/Mathematics/Discrete/CellularAutomata/">Cellular automata: Mathematica notebooks</a>
%H A051023 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A051023 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F A051023 a(n) = A070950(n,n). - _Reinhard Zumkeller_, Jun 06 2013
%F A051023 a(n) = 1 - A226474(n). - _Reinhard Zumkeller_, Jun 08 2013
%F A051023 From _Antti Karttunen_, Oct 04 2019: (Start)
%F A051023 a(n) = A000035(floor(A110240(n) / 2^n)).
%F A051023 For n>= 2, a(n) = (A328100(n) OR A328101(n)) XOR A328101(1+n). ["Sideways evaluation"]
%F A051023 (End)
%t A051023 CellularAutomaton[30, {{1}, 0}, 101, {All, {0}}]//Flatten
%o A051023 (Haskell)
%o A051023 a051023 n = a070950 n n  -- _Reinhard Zumkeller_, Jun 06 2013
%o A051023 (PARI)
%o A051023 A051023(n) = ((A110240(n)>>n)%2);
%o A051023 \\ Or for fast creation of b-files:
%o A051023 A051023write(up_to) = { my(s=1, n=0); for(n=0,up_to, write("b051023.txt", n, " ", ((s>>n)%2)); s = A269160(s)); }; \\ _Antti Karttunen_, Oct 03 2019
%Y A051023 Cf. A070950, A269160 (rule 30), A071032, A269161 (rule 86).
%Y A051023 Cf. A000035, A092539, A226474.
%Y A051023 Cf. A327974 (adjacent bits xored), A327982 (partial sums), A327983 (run lengths).
%Y A051023 Characteristic function of A327984 (gives the positions of ones in this sequence), A327985 (positions of zeros).
%Y A051023 Cf. also A328100, A328101, A328102 (neighbor columns).
%Y A051023 Cf. A365254 (converted to base 10).
%K A051023 nonn
%O A051023 0,1
%A A051023 _Eric W. Weisstein_
%E A051023 Corrected from 64th term by Daniel B. Cristofani (cristofd(AT)hevanet.com), Jan 07 2004