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%I #4 Jun 28 2017 13:23:44
%S 1,2,4,5,6,7,8,9,11,12,13,15,16,19,20,22,23,26,27,29,31,32,33,34,37,
%T 38,40,42,43,44,45,48,51,52,54,55,56,58,60,61,62,63,66,69,70,72,73,74,
%U 76,78,79,80,82,83,84,85,88,89,91,92,95,98,99,101,102,103
%N Positions of 0 in A289104; complement of A289106.
%C Conjecture: a(n)/n -> (1 + sqrt(5))/2 = golden ratio = tau, and 1 < a(n)/n < tau for n >= 1.
%H Clark Kimberling, <a href="/A289105/b289105.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" -> "011", "10" -> "000"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289104 *)
%t Flatten[Position[st, 0]] (* A289105 *)
%t Flatten[Position[st, 1]] (* A289106 *)
%Y Cf. A001622, A289105, A289106.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 28 2017
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