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Positions of 1 in A288733; complement of A288734.
3

%I #10 Oct 08 2017 12:45:47

%S 1,5,7,8,10,11,15,19,21,22,24,25,27,28,30,31,35,39,41,42,44,45,49,53,

%T 55,56,58,59,61,62,64,65,67,68,70,71,75,79,81,82,84,85,89,93,95,96,98,

%U 99,101,102,104,105,109,113,115,116,118,119,123,127,129,130

%N Positions of 1 in A288733; complement of A288734.

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

%H Clark Kimberling, <a href="/A288735/b288735.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[21]] - 48 (* A288733 *)

%t Flatten[Position[st, 0]] (* A288734 *)

%t Flatten[Position[st, 1]] (* A288735 *)

%Y Cf. A288733, A288734.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 16 2017