A059539 Beatty sequence for 3^(1/3).

1, 2, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 25, 27, 28, 30, 31, 33, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 64, 66, 67, 69, 70, 72, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99, 100

Offset: 1

Author

Mitch Harris, Jan 22 2001

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 1..2000
• Aviezri S. Fraenkel, Jonathan Levitt, and Michael Shimshoni, Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no.4, 335-345.
• Eric Weisstein's World of Mathematics, Beatty Sequence
• Index entries for sequences related to Beatty sequences

Crossrefs

Beatty complement is A059540.

Partial sums of A081129.

Cf. A002581.

Programs

Mathematica

Floor[Range[100]*CubeRoot[3]] (* Paolo Xausa, Jul 05 2024 *)

PARI

{ default(realprecision, 100); b=3^(1/3); for (n = 1, 2000, write("b059539.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 27 2009

Python

from sympy import integer_nthroot
def A059539(n): return integer_nthroot(3*n**3,3)[0] # Chai Wah Wu, Mar 16 2021

Formula

a(n) = floor(n*A002581). - R. J. Mathar, Apr 12 2019