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Positions of 1 in A288736; complement of A288737.
3

%I #8 Aug 04 2018 04:11:08

%S 2,3,8,9,11,12,14,15,20,21,26,27,29,30,32,33,35,36,38,39,44,45,50,51,

%T 53,54,56,57,62,63,68,69,71,72,74,75,77,78,80,81,83,84,86,87,92,93,98,

%U 99,101,102,104,105,110,111,116,117,119,120,122,123,125,126

%N Positions of 1 in A288736; complement of A288737.

%C Conjecture: a(n)/n -> 2, and -2/3 < 2 - a(n)/n) < 1/2 for n >= 1.

%H Clark Kimberling, <a href="/A288740/b288740.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" -> "1000", "10" -> "01"}]

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

%t st = ToCharacterCode[w[22]] - 48 (* A288736 *)

%t Flatten[Position[st, 0]] (* A288737 *)

%t Flatten[Position[st, 1]] (* A288740 *)

%Y Cf. A288736, A288737.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 16 2017