A289175 - OEIS

%I #4 Jun 29 2017 14:56:34

%S 1,2,4,5,9,10,12,16,17,19,20,22,26,27,28,29,31,32,37,40,41,43,45,46,

%T 47,48,50,54,58,62,63,65,66,67,68,70,71,72,74,75,80,85,90,94,95,96,97,

%U 99,100,101,103,104,107,108,110,111,115,116,119,125,131,136

%N Positions of 0 in A289174; complement of A289176.

%C Conjecture:  a(n)/n -> 2.2..., and if m denotes this number, then -1 < m - a(n)/n < m - 1 for n >= 1.

%H Clark Kimberling, <a href="/A289175/b289175.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" -> "011"}]

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

%t st = ToCharacterCode[w[z]] - 48   (* A289174 *)

%t Flatten[Position[st, 0]]  (* A289175 *)

%t Flatten[Position[st, 1]]  (* A289176 *)

%Y Cf. A289174, A289176, A289177.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 29 2017