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%I #4 Jun 28 2017 22:26:15
%S 1,2,4,5,7,8,11,12,14,16,18,19,22,25,28,29,31,33,35,37,39,41,43,44,47,
%T 50,53,56,59,62,65,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,97,
%U 100,103,106,109,112,115,118,121,124,127,130,133,136,139
%N Positions of 0 in A289128; complement of A289130.
%C Conjecture: a(n)/n -> 5/2..., and 0 < 5/2 - a(n)/n < 3/2 for n >= 1.
%H Clark Kimberling, <a href="/A289129/b289129.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" -> "010"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289128 *)
%t Flatten[Position[st, 0]] (* A289129 *)
%t Flatten[Position[st, 1]] (* A289130 *)
%Y Cf. A289128, A289130.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 28 2017
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