A289244 - OEIS

%I #7 Jul 01 2017 23:04:39

%S 3,5,8,11,16,18,23,25,28,33,37,39,42,45,50,54,56,61,63,66,69,74,76,81,

%T 83,88,90,93,98,102,104,107,110,115,117,122,124,127,132,136,138,141,

%U 146,148,151,156,158,163,165,170,172,175,180,182,185,190,194,196

%N Positions of 1 in A289242; complement of A289243.

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

%H Clark Kimberling, <a href="/A289244/b289244.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" -> "100"}]

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

%t st = ToCharacterCode[w[z]] - 48   (* A289242 *)

%t Flatten[Position[st, 0]]  (* A289243 *)

%t Flatten[Position[st, 1]]  (* A289244 *)

%Y Cf. A289242, A289243.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 01 2017