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%I #4 May 13 2017 17:21:46
%S 5,11,19,25,33,39,45,53,59,67,73,79,87,93,101,107,115,121,127,135,141,
%T 149,155,161,169,175,183,189,197,203,209,217,223,231,237,243,251,257,
%U 265,271,277,285,291,299,305,313,319,325,333,339,347,353,359,367,373
%N Positions of 1 in A286688; complement of A286689.
%C a(n) - a(n-1) is in {1,2,3} for n>=2, and a(n)/n -> 4 + sqrt(8).
%H Clark Kimberling, <a href="/A286690/b286690.txt">Table of n, a(n) for n = 1..10000</a>
%e As a word, A286688 = 00001000001000000010000010..., in which 1 is in positions 5,11,19,25,...
%t s = Nest[Flatten[# /. {0 -> {0, 0, 1}, 1 -> {0}}] &, {0}, 6] (* A171588 *)
%t w = StringJoin[Map[ToString, s]]
%t w1 = StringReplace[w, {"0" -> "00", "1"->"10"}]
%t st = ToCharacterCode[w1] - 48 ; (* A286688 *)
%t Flatten[Position[st, 0]]; (* A286689 *)
%t Flatten[Position[st, 1]]; (* A286690 *)
%Y Cf. A171588, A286688, A286689.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 13 2017