A287676 - OEIS

%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