A286990 - OEIS

%I #5 May 20 2017 10:20:45

%S 1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,1,

%T 0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,

%U 0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,1,0

%N {0->010, 1->101}-transform of the Sturmian word A080764.

%C A080764 = 1101101110110111011011011101..., and replacing each 0 by 010 and each 1 by 101 gives 101101010101101010101101101010101..., in which the positions of 0 are given by A286991, and of 1, by A286992.

%H Clark Kimberling, <a href="/A286990/b286990.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, A286991, A286992.

%K nonn,easy

%O 1

%A _Clark Kimberling_, May 19 2017