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Positions of 1 in A286691; complement of A286692.
3

%I #4 May 14 2017 15:53:16

%S 2,5,7,8,11,14,16,17,20,23,26,28,29,32,35,37,38,41,44,47,49,50,53,56,

%T 58,59,62,65,67,68,71,74,77,79,80,83,86,88,89,92,95,98,100,101,104,

%U 107,109,110,113,116,118,119,122,125,128,130,131,134,137,139,140

%N Positions of 1 in A286691; complement of A286692.

%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="/A286693/b286693.txt">Table of n, a(n) for n = 1..10000</a>

%e As a word, A286691 = 0100101100100101100100100101100100..., in which 1 is in positions 2,5,7,8,11,...

%t s = Nest[Flatten[# /. {0 -> {0, 0, 1}, 1 -> {0}}] &, {0}, 6] (* A171588 *)

%t w = StringJoin[Map[ToString, s]]

%t w1 = StringReplace[w, {"0" -> "010", "1"->"110"}]

%t st = ToCharacterCode[w1] - 48 ; (* A286691 *)

%t Flatten[Position[st, 0]]; (* A286692 *)

%t Flatten[Position[st, 1]]; (* A286693 *)

%Y Cf. A171588, A286691, A286692.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, May 14 2017