A288998 - OEIS

%I #4 Jun 25 2017 23:01:55

%S 1,2,4,5,6,8,9,11,12,13,15,16,18,19,21,22,23,25,26,28,29,30,32,33,35,

%T 36,38,39,40,42,43,45,46,47,49,50,52,53,54,56,57,59,60,62,63,64,66,67,

%U 69,70,71,73,74,76,77,79,80,81,83,84,86,87,88,90,91,93

%N Positions of 0 in A288997; complement of A288999.

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

%H Clark Kimberling, <a href="/A288998/b288998.txt">Table of n, a(n) for n = 1..10000</a>

%t z = 10; (* 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" -> "001"}]

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

%t st = ToCharacterCode[w[z]] - 48   (* A288997 *)

%t Flatten[Position[st, 0]]  (* A288998 *)

%t Flatten[Position[st, 1]]  (* A288999 *)

%Y Cf. A288997, A288999.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 25 2017