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%I #4 Jun 28 2017 13:23:00
%S 3,5,8,12,16,19,23,26,30,32,37,39,43,47,50,53,57,61,63,66,71,73,78,80,
%T 84,88,90,95,97,102,104,107,111,115,119,121,124,129,132,135,139,142,
%U 146,149,152,156,160,162,165,170,173,176,180,182,187,189,194,196
%N Positions of 1 in A289071; complement of A289072.
%C Conjecture: a(n)/n -> 2 + sqrt(2), and 0 < 2 + sqrt(2) - a(n)/n < 1 for n >= 1. .
%H Clark Kimberling, <a href="/A289073/b289073.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" -> "010", "10" -> "100"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289071 *)
%t Flatten[Position[st, 0]] (* A289072 *)
%t Flatten[Position[st, 1]] (* A289073 *)
%Y Cf. A289071, A289072.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jun 27 2017