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%I #4 May 07 2017 21:36:05
%S 2,3,6,8,10,11,14,16,18,19,22,24,26,28,29,32,34,35,38,40,42,43,46,48,
%T 50,51,54,56,57,60,62,64,66,67,70,72,74,75,78,80,82,83,86,88,90,92,93,
%U 96,98,99,102,104,106,108,109,112,114,116,117,120,122,124
%N Positions of 1 in A286049; complement of A286050.
%C Conjecture: 2n - a(n) is in {0,1} for n >= 1.
%C Also, the positions of 1 in the {100->0}-transform of A010060.
%H Clark Kimberling, <a href="/A286051/b286051.txt">Table of n, a(n) for n = 1..10000</a>
%e As a word, A286049 = 0110010101100101..., in which 1 is in positions 2,3,6,8,10,...
%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* Thue-Morse, A010060 *)
%t w = StringJoin[Map[ToString, s]]
%t w1 = StringReplace[w, {"110" -> "1"}]
%t st = ToCharacterCode[w1] - 48 (* A286049 *)
%t Flatten[Position[st, 0]] (* A286050 *)
%t Flatten[Position[st, 1]] (* A286051 *)
%Y Cf. A010060, A286049, A286050.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 07 2017
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