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Positions of 0 in A288520; complement of A288522.
3

%I #6 Jun 13 2017 23:00:06

%S 1,2,4,5,7,8,10,11,13,15,17,18,20,22,24,25,27,29,31,32,33,35,36,37,39,

%T 40,42,44,46,47,48,50,51,52,54,55,57,59,61,62,63,65,66,67,69,70,71,73,

%U 74,76,77,79,80,81,83,84,86,87,89,90,92,94,96,97,98,100

%N Positions of 0 in A288520; complement of A288522.

%C Conjecture: a(n)/n -> 1.52..., and if m denotes this number, then -1 < m - a(n)/n < 1 for n >= 1.

%H Clark Kimberling, <a href="/A288521/b288521.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", "10" -> "010"}]

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

%t st = ToCharacterCode[w[18]] - 48 (* A288520 *)

%t Flatten[Position[st, 0]] (* A288521 *)

%t Flatten[Position[st, 1]] (* A288522 *)

%Y Cf. A288520, A288522.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 13 2017