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A269164 Numbers not in range of A269160; indices of zeros in A269162 from n >= 1 onward.

%I A269164 #20 Feb 16 2025 08:33:30
%S A269164 1,2,3,4,5,6,8,9,10,11,12,15,16,17,18,19,20,21,22,23,24,29,30,31,32,
%T A269164 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,55,57,58,59,60,61,62,
%U A269164 64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96
%N A269164 Numbers not in range of A269160; indices of zeros in A269162 from n >= 1 onward.
%C A269164 Natural numbers n for which there does not exist any number k such that A269160(k) = n.
%C A269164 These are binary representations (shown in decimal) of Garden of Eden patterns in Wolfram's Rule 30 cellular automaton if infinite predecessors are forbidden.
%H A269164 Antti Karttunen, <a href="/A269164/b269164.txt">Table of n, a(n) for n = 1..12285</a>
%H A269164 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30</a>
%H A269164 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269164 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A269164 Other identities. For all n >= 1:
%F A269164 A269169(a(n)) = n.
%t A269164 terms = 100; Clear[f]; f[max_] := f[max] = (s = Sort[Table[BitXor[n, BitOr[2n, 4n]], {n, 0, max}]]; Complement[Range[Last[s]], s][[1 ;; terms ]]); f[terms]; f[max = 2 terms]; While[Print[max]; f[max] != f[max/2], max = 2 max]; A269164 = f[max] (* _Jean-François Alcover_, Feb 23 2016 *)
%o A269164 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A269164 (define A269164 (MATCHING-POS 1 1 (lambda (n) (zero? (A269162 n)))))
%Y A269164 Complement: A269163.
%Y A269164 Indices of zeros in A269162 and A269166 (after the initial zero).
%Y A269164 Cf. A269169 (left inverse).
%Y A269164 Cf. A269160, A269168.
%K A269164 nonn
%O A269164 1,2
%A A269164 _Antti Karttunen_, Feb 20 2016