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Positions of 0 in A288694; complement of A288696.
3

%I #4 Jun 16 2017 22:22:38

%S 1,4,5,6,9,12,13,16,17,18,21,22,23,26,29,30,31,34,37,38,41,42,43,46,

%T 49,50,53,54,55,58,59,60,63,66,67,70,71,72,75,76,77,80,83,84,85,88,91,

%U 92,95,96,97,100,101,102,105,108,109,110,113,116,117

%N Positions of 0 in A288694; complement of A288696.

%C Conjecture: a(n)/n ->1.93..., and if m denotes this number, then -1 < m - a(n)/n) < 1 for n >= 1.

%H Clark Kimberling, <a href="/A288695/b288695.txt">Table of n, a(n) for n = 1..10000</a>

%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "10" -> "100"}]

%t Table[w[n], {n, 0, 8}]

%t st = ToCharacterCode[w[11]] - 48 (* A288694 *)

%t Flatten[Position[st, 0]] (* A288695 *)

%t Flatten[Position[st, 1]] (* A288696 *)

%t Table[StringLength[w[n]], {n, 1, 35}]

%Y Cf. A288694, A288696.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 16 2017