%I #7 Jul 01 2017 23:04:17
%S 1,2,4,5,7,9,10,12,13,14,15,17,18,20,21,22,24,26,27,28,29,31,32,34,35,
%T 36,38,39,41,42,44,45,46,48,50,51,52,53,55,56,58,59,60,62,63,65,67,68,
%U 69,70,72,73,75,76,77,79,80,82,83,85,86,87,89,91,92,93
%N Positions of 0 in A289239; complement of A289241.
%C Conjecture: a(n)/n -> sqrt(2)..., and -1 < sqrt(2)-a(n)/n < = -1+sqrt(2) for n >= 1.
%H Clark Kimberling, <a href="/A289240/b289240.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" -> "010"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289239 *)
%t Flatten[Position[st, 0]] (* A289240 *)
%t Flatten[Position[st, 1]] (* A289241 *)
%Y Cf. A289239, A289241.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jul 01 2017
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