%I #4 Jun 28 2017 13:23:23

%S 3,5,8,12,13,16,19,20,21,25,26,29,31,32,33,38,40,41,45,46,48,49,50,51,

%T 56,59,60,62,63,64,69,71,72,75,76,77,78,83,86,87,90,92,93,96,97,98,

%U 103,106,107,109,110,111,115,116,117,118,119,124,127,128,131

%N Positions of 1 in A289074; complement of A289075.

%C Conjecture: a(n)/n -> 2.05..., and if m denotes this number, then -1 < m - a(n)/n < 0 for n >= 1.

%H Clark Kimberling, <a href="/A289076/b289076.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" -> "100"}]

%t TableForm[Table[w[n], {n, 0, 10}]]

%t st = ToCharacterCode[w[z]] - 48 (* A289074 *)

%t Flatten[Position[st, 0]] (* A289075 *)

%t Flatten[Position[st, 1]] (* A289076 *)

%Y Cf. A289074, A289075.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 28 2017