%I #7 Jul 01 2017 23:04:26

%S 3,6,8,11,16,19,23,25,30,33,37,40,43,47,49,54,57,61,64,66,71,74,78,81,

%T 84,88,90,95,98,102,105,107,110,115,119,122,124,129,131,136,139,141,

%U 146,148,151,156,160,163,165,170,172,177,180,183,185,190,194,197

%N Positions of 1 in A289239; complement of A289240.

%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="/A289241/b289241.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, A289240.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 01 2017