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%I #6 Jun 28 2017 22:26:24
%S 3,6,9,10,13,15,17,20,21,23,24,26,27,30,32,34,36,38,40,42,45,46,48,49,
%T 51,52,54,55,57,58,60,61,63,64,67,69,71,73,75,77,79,81,83,85,87,89,91,
%U 93,95,98,99,101,102,104,105,107,108,110,111,113,114,116
%N Positions of 1 in A289128; complement of A289129.
%C Conjecture: a(n)/n -> 5/3..., and -4/3 < 5/3 - a(n)/n < 0 for n >= 1.
%H Clark Kimberling, <a href="/A289130/b289130.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, A289129.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jun 28 2017
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