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

Author

Benoit Cloitre, Apr 16 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A059539, A081117, A081147, A081168.

Programs

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

Mathematica

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

PARI

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

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

Formula

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