A289013 - OEIS

%I #6 Jun 26 2017 22:16:27

%S 3,5,8,13,16,20,22,27,30,34,37,40,44,46,51,54,58,61,63,68,71,75,78,81,

%T 85,87,92,95,99,102,104,107,112,116,119,121,126,128,133,136,138,143,

%U 145,148,153,157,160,162,167,169,174,177,180,182,187,191,194,198

%N Positions of 1 in A289011; complement of A289012.

%C Conjecture: a(n)/n -> 2 + sqrt(2), and 0 < 2 + sqrt(2) - a(n)/n < 1 for n >= 1.

%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" -> "001", "10" -> "100"}]

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

%t st = ToCharacterCode[w[z]] - 48   (* A289011 *)

%t Flatten[Position[st, 0]]  (* A289012 *)

%t Flatten[Position[st, 1]]  (* A289013 *)

%Y Cf. A289011, A289012.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 26 2017