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%I #4 Jun 27 2017 21:37:39
%S 1,2,4,5,7,8,10,11,12,14,15,17,18,19,21,22,24,25,27,28,29,31,32,34,35,
%T 36,38,39,41,42,44,45,46,48,49,51,52,53,55,56,58,59,60,62,63,65,66,68,
%U 69,70,72,73,75,76,77,79,80,82,83,85,86,87,89,90,92,93
%N Positions of 0 in A289035; complement of A289037.
%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="/A289036/b289036.txt">Table of n, a(n) for n = 1..10000</a>
%t z = 10; (* number of iterates *)
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "010"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289035 *)
%t Flatten[Position[st, 0]] (* A289036 *)
%t Flatten[Position[st, 1]] (* A289037 *)
%Y Cf. A289035, A289037.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 27 2017
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