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%I #4 Jun 29 2017 14:56:07
%S 1,2,4,5,6,8,9,11,12,13,16,17,18,19,21,23,24,25,26,28,29,31,33,34,36,
%T 37,38,39,41,42,43,45,46,47,50,51,53,54,55,56,58,59,60,62,63,65,67,68,
%U 69,70,72,74,75,76,77,79,81,82,83,84,87,88,89,90,92,93
%N Positions of 0 in A289165; complement of A289167.
%C Conjecture: a(n)/n -> 1.42..., and if m denotes this number, then -1 < m - a(n)/n < m - 1 for n >= 1.
%H Clark Kimberling, <a href="/A289166/b289166.txt">Table of n, a(n) for n = 1..10000</a>
%t z = 11; (* number of iterates *)
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "100", "10" -> "001"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289165 *)
%t Flatten[Position[st, 0]] (* A289166 *)
%t Flatten[Position[st, 1]] (* A289167 *)
%Y Cf. A289165, A289167.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 29 2017