%I #6 Jun 26 2017 22:15:39
%S 1,2,4,5,8,9,11,14,15,17,18,20,23,24,26,27,29,30,34,37,38,40,41,43,44,
%T 47,48,51,55,58,59,61,62,64,65,68,69,71,74,75,77,82,86,89,90,92,93,95,
%U 96,99,100,102,105,106,108,109,111,114,115,117,118,122,127
%N Positions of 0 in A289007; complement of A289009.
%C Conjecture: a(n)/n -> 2.37..., and if m denotes this number, then 0 < m - a(n)/n < 2 for n >= 1.
%H Clark Kimberling, <a href="/A289008/b289008.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" -> "001", "10" -> "011"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289007 *)
%t Flatten[Position[st, 0]] (* A289008 *)
%t Flatten[Position[st, 1]] (* A289009 *)
%Y Cf. A289007, A289009.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 26 2017