A286904 Positions of 0 in A286903; complement of A286905.

3, 4, 7, 8, 12, 13, 16, 17, 21, 22, 25, 26, 29, 30, 34, 35, 38, 39, 43, 44, 47, 48, 51, 52, 56, 57, 60, 61, 65, 66, 69, 70, 74, 75, 78, 79, 82, 83, 87, 88, 91, 92, 96, 97, 100, 101, 104, 105, 109, 110, 113, 114, 118, 119, 122, 123, 127, 128, 131, 132, 135

Offset

1,1

Comments

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

Links

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

Formula

From Ridouane Oudra, Feb 17 2025 : (Start)

a(n) = floor((n + (n mod 2))*r) + n, where r = (1+sqrt(2))/2.

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

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

Example

As a word, A286804 = 11001100111001100111001..., in which 0 is in positions 3,4,7,8,12,...

Mathematica

s = Nest[Flatten[# /. {0 -> 1, 1 -> {1, 1, 0}}] &, {1}, 7] (* A080764 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0" -> "00"}]
st = ToCharacterCode[w1] - 48 ; (* A286903 *)
Flatten[Position[st, 0]];  (* A286904 *)
Flatten[Position[st, 1]];  (* A286905 *)

Crossrefs

Cf. A080764, A286903, A286905.

Sequence in context: A211220 A051201 A026449 * A282166 A165157 A182079

Adjacent sequences: A286901 A286902 A286903 * A286905 A286906 A286907

Keyword

nonn,easy,changed

Author

Clark Kimberling, May 17 2017

Status

approved