A286997 Positions of 0 in A286996; complement of A188383.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76

Offset

1,2

Comments

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

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

As a word, A286993 = 11000110001000110..., in which 0 is in positions 1,2,3,4,5,6,8,....

Mathematica

s = Nest[Flatten[# /. {0 -> 1, 1 -> {1, 1, 0}}] &, {1}, 11]; (* Sturmian word A080764 *)
w = StringJoin[Map[ToString, s]];
w1 = StringReplace[w, {"0" -> "000", "11"->""}]
st = ToCharacterCode[w1] - 48 ; (* A286996 *)
Flatten[Position[st, 0]];  (* A286997 *)
Flatten[Position[st, 1]];  (* A188383 *)

Crossrefs

Cf. A080764, A286996, A188383.

Sequence in context: A367906 A022551 A172251 * A187396 A020659 A047304

Adjacent sequences: A286994 A286995 A286996 * A286998 A286999 A287000

Keyword

nonn,easy

Author

Clark Kimberling, May 20 2017

Status

approved