A286923 Positions of 0 in A286922; complement of A286924.

3, 7, 12, 16, 21, 25, 29, 34, 38, 43, 47, 51, 56, 60, 65, 69, 74, 78, 82, 87, 91, 96, 100, 104, 109, 113, 118, 122, 127, 131, 135, 140, 144, 149, 153, 157, 162, 166, 171, 175, 179, 184, 188, 193, 197, 202, 206, 210, 215, 219, 224, 228, 232, 237, 241, 246

Offset

1,1

Comments

a(n) - a(n-1) is in {4,5} for n>=2, and a(n)/n -> 3 + sqrt(2).

Links

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

Formula

From Ridouane Oudra, Nov 02 2024: (Start)

a(n) = floor((3+sqrt(2))*n - 1).

a(n) = floor(sqrt(2)*n) + 3*n - 1.

a(n) = A001951(n) + A008585(n) - 1

a(n) = A187338(n) - 1. (End)

Example

As a word, A286922 = 1101110111101110111101110..., in which 0 is in positions 3,7,12,16....

Maple

seq(floor((3+sqrt(2))*n)-1, n=1..80); # Ridouane Oudra, Nov 02 2024

Mathematica

s = Nest[Flatten[# /. {0 -> 1, 1 -> {1, 1, 0}}] &, {1}, 7] (* A080764 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0" -> "01"}]
st = ToCharacterCode[w1] - 48 ; (* A286922 *)
Flatten[Position[st, 0]];  (* A286923 *)
Flatten[Position[st, 1]];  (* A286924 *)

Crossrefs

Cf. A080764, A286922, A286924, A001951, A187338, A008585.

Sequence in context: A310241 A310242 A310243 * A330185 A330181 A184917

Adjacent sequences: A286920 A286921 A286922 * A286924 A286925 A286926

Keyword

nonn,easy

Author

Clark Kimberling, May 17 2017

Status

approved