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%I #4 Jun 29 2017 14:56:14
%S 3,7,10,14,15,20,22,27,30,32,35,40,44,48,49,52,57,61,64,66,71,73,78,
%T 80,85,86,91,95,99,102,106,107,110,115,119,123,126,129,131,134,139,
%U 143,145,148,151,153,158,160,165,167,172,176,179,181,184,185,190,194
%N Positions of 1 in A289165; complement of A289166.
%C Conjecture: a(n)/n -> 3.35..., and if m denotes this number, then -1 < m - a(n)/n < 1 for n >= 1.
%H Clark Kimberling, <a href="/A289167/b289167.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, A289166.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jun 29 2017