%I #10 Nov 23 2024 00:28:40
%S 1,2,4,7,8,11,14,15,17,20,23,24,27,30,31,33,36,37,40,43,44,47,50,51,
%T 53,56,59,60,63,66,67,69,72,73,76,79,80,82,85,88,89,92,95,96,98,101,
%U 104,105,108,111,112,114,117,118,121,124,125,128,131,132,134,137
%N Positions of 0 in A286059; complement of A286061.
%C Conjecture: lim_{n->oo} a(n)/n = 2.24..., and if m denotes this number, then -1 < a(n)/n - m < 2 for n >= 1.
%H Clark Kimberling, <a href="/A286060/b286060.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" -> "001", "1" -> "011"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[11]] - 48 (* A286059 *)
%t Flatten[Position[st, 0]] (* A286060 *)
%t Flatten[Position[st, 1]] (* A286061 *)
%t Table[StringLength[w[n]], {n, 1, 35}] (* A286062 conjectured *)
%Y Cf. A286059, A286061, A286062.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 05 2017