%I #4 Jun 25 2017 23:01:29
%S 1,2,4,5,6,7,8,9,11,12,13,15,16,17,19,20,22,23,24,26,27,29,30,31,33,
%T 34,36,37,38,39,40,41,43,44,45,46,47,48,50,51,53,54,55,57,58,60,61,62,
%U 63,64,65,67,68,69,71,72,73,75,76,78,79,80,82,83,84,86,87
%N Positions of 0 in A288991; complement of A288993.
%C Conjecture: a(n)/n -> 1.28... and if m denotes this number, then -1 < m - a(n)/n < 1 for n >= 1.
%H Clark Kimberling, <a href="/A288992/b288992.txt">Table of n, a(n) for n = 1..10000</a>
%t z = 10; (* number of iterates *)
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "000"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A288991 *)
%t Flatten[Position[st, 0]] (* A288992 *)
%t Flatten[Position[st, 1]] (* A288993 *)
%Y Cf. A288991, A288993.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 25 2017