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%I #4 May 09 2017 17:40:01
%S 2,3,4,5,6,9,11,12,13,14,16,17,20,21,22,23,24,27,29,30,33,34,35,36,38,
%T 39,40,41,42,45,47,48,49,50,52,53,56,57,58,59,61,62,63,64,65,68,70,71,
%U 74,75,76,77,78,81,83,84,85,86,88,89,92,93,94,95,96,99
%N Positions of 1 in A286419; complement of A286420.
%C a(n) - a(n-1) is in {1,2,3} for n>=2. Conjecture: a(n)/n -> 3/2.
%H Clark Kimberling, <a href="/A286421/b286421.txt">Table of n, a(n) for n = 1..10000</a>
%e As a word, A286419 = 011111001011110110011..., in which 1 is in positions 2,3,4,5,6,9,...
%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* A010060 *)
%t w = StringJoin[Map[ToString, s]]
%t w1 = StringReplace[w, {"0100" -> "1"}]
%t st = ToCharacterCode[w1] - 48 (* A286419 *)
%t Flatten[Position[st, 0]] (* A286420 *)
%t Flatten[Position[st, 1]] (* A286421 *)
%Y Cf. A010060, A286419, A286420.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 09 2017
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