A081129 Differences of Beatty sequence for cube root of 3.

1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

a(n) = floor((n+1)*3^(1/3)) - floor(n*3^(1/3)).

Mathematica

Differences[Floor[Range[0, 110]Surd[3, 3]]] (* Harvey P. Dale, Apr 06 2022 *)

Prog

(PARI) a(n)=floor((n+1)*3^(1/3))-floor(n*3^(1/3))
(Magma)
A081129:= func< n | Floor((n+1)*3^(1/3)) - Floor(n*3^(1/3)) >;
[A081129(n): n in [0..120]]; // G. C. Greubel, Jan 15 2024
(SageMath)
def A081129(n): return floor((n+1)*3^(1/3)) - floor(n*3^(1/3))
[A081129(n) for n in range(121)] # G. C. Greubel, Jan 15 2024

Crossrefs

Cf. A059539, A081117, A081147, A081168.

Sequence in context: A356112 A232740 A188512 * A022934 A107450 A341765

Adjacent sequences: A081126 A081127 A081128 * A081130 A081131 A081132

Keyword

nonn

Author

Benoit Cloitre, Apr 16 2003

Status

approved