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Positions of 1 in A288473; complement of A288474.
3

%I #12 Jun 13 2017 23:03:11

%S 2,4,6,7,9,10,12,14,16,17,19,20,22,24,26,27,29,30,33,34,36,37,39,41,

%T 43,44,46,47,50,51,53,54,56,58,60,61,63,64,66,68,70,71,73,74,76,78,80,

%U 81,83,84,87,88,90,91,93,95,97,98,100,101,104,105,107,108

%N Positions of 1 in A288473; complement of A288474.

%C Conjecture: a(n)/n -> 1.74..., and if m denotes this number, then -1 < m - a(n)/n < 1 for n >= 1.

%H Clark Kimberling, <a href="/A288475/b288475.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" -> "0101", "1" -> "011"}]

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

%t st = ToCharacterCode[w[11]] - 48 (* A288473 *)

%t Flatten[Position[st, 0]] (* A288474 *)

%t Flatten[Position[st, 1]] (* A288475 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A288476 conjectured *)

%Y Cf. A288473, A288474, A288476.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 11 2017