A289243 - OEIS

%I #8 Jul 01 2017 23:04:33

%S 1,2,4,6,7,9,10,12,13,14,15,17,19,20,21,22,24,26,27,29,30,31,32,34,35,

%T 36,38,40,41,43,44,46,47,48,49,51,52,53,55,57,58,59,60,62,64,65,67,68,

%U 70,71,72,73,75,77,78,79,80,82,84,85,86,87,89,91,92,94

%N Positions of 0 in A289242; complement of A289244.

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

%H Clark Kimberling, <a href="/A289243/b289243.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, A289244.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jul 01 2017