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%I #17 Oct 23 2023 01:43:00
%S 1,4,5,6,9,10,13,14,15,18,19,20,23,24,27,28,29,32,33,36,37,38,41,42,
%T 43,46,47,50,51,52,55,56,57,60,61,64,65,66,69,70,73,74,75,78,79,80,83,
%U 84,87,88,89,92,93,96,97,98,101,102,103,106,107,110,111,112
%N Positions of 1 in A287674; complement of A287675.
%C Conjecture: -1 < n*r - a(n) < 2 for n >= 1, where r = 4 - sqrt(5).
%H Clark Kimberling, <a href="/A287676/b287676.txt">Table of n, a(n) for n = 1..10000</a>
%F Conjecture: a(n) = 5*n + 2 - 2 * floor((n+1)*phi), where phi is the golden mean. - _Chunqing Liu_, Sep 27 2023
%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 10] (* A003849 *)
%t w = StringJoin[Map[ToString, s]]
%t w1 = StringReplace[w, {"0" -> "1", "1" -> "001"}]
%t st = ToCharacterCode[w1] - 48 (* A287674 *)
%t Flatten[Position[st, 0]] (* A287675 *)
%t Flatten[Position[st, 1]] (* this sequence *)
%Y Cf. A001622, A003849, A287674, A287675.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 02 2017
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