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%I #6 Jun 26 2017 22:16:43
%S 1,2,4,5,6,7,8,9,11,12,13,15,16,18,19,20,22,23,25,26,27,29,30,31,32,
%T 33,34,36,37,38,39,40,42,43,44,46,47,49,50,51,53,54,55,57,58,59,61,62,
%U 63,64,65,66,68,69,70,72,73,74,75,76,77,79,80,81,82,83,85
%N Positions of 0 in A289016; complement of A289018.
%C Conjecture: a(n)/n -> 1.28..., and if m denotes this number, then -1 < m - a(n)/n < -1 + m for n >= 1.
%H Clark Kimberling, <a href="/A289017/b289017.txt">Table of n, a(n) for n = 1..10000</a>
%t z = 11; (* number of iterates *)
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "000"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289016 *)
%t Flatten[Position[st, 0]] (* A289017 *)
%t Flatten[Position[st, 1]] (* A289018 *)
%Y Cf. A289016, A289018.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 26 2017
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