A286992 - OEIS

%I #4 May 20 2017 10:21:00

%S 1,3,4,6,8,10,12,13,15,17,19,21,22,24,25,27,29,31,33,34,36,38,40,42,

%T 43,45,46,48,50,52,54,55,57,59,61,63,64,66,68,70,72,73,75,76,78,80,82,

%U 84,85,87,89,91,93,94,96,97,99,101,103,105,106,108,110,112

%N Positions of 1 in A286990; complement of A286991.

%C a(n) - a(n-1) is in {1,2} for n>=2, and a(n)/n -> 6- 3*sqrt(2).

%C As a word, A286990 = 1011010101011010101011..., in which 1 is in positions 1,3,4,6,8,....

%H Clark Kimberling, <a href="/A286992/b286992.txt">Table of n, a(n) for n = 1..10000</a>

%t s = Nest[Flatten[# /. {0 -> 1, 1 -> {1, 1, 0}}] &, {1}, 11]; (* Sturmian word A080764 *)

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

%t w1 = StringReplace[w, {"0" -> "010", "1"->"101"}]

%t st = ToCharacterCode[w1] - 48 ; (* A286990 *)

%t Flatten[Position[st, 0]];  (* A286991 *)

%t Flatten[Position[st, 1]];  (* A286992 *)

%Y Cf. A080764, A286990, A286991.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 19 2017