A022842 Beatty sequence for sqrt(8).

2, 5, 8, 11, 14, 16, 19, 22, 25, 28, 31, 33, 36, 39, 42, 45, 48, 50, 53, 56, 59, 62, 65, 67, 70, 73, 76, 79, 82, 84, 87, 90, 93, 96, 98, 101, 104, 107, 110, 113, 115, 118, 121, 124, 127, 130, 132, 135, 138, 141, 144, 147, 149, 152, 155, 158, 161, 164

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)
• Index entries for sequences related to Beatty sequences

Crossrefs

A bisection of A001951. Cf. A010466.

Programs

Magma

[Floor(n*Sqrt(8)): n in [1..60]]; // Vincenzo Librandi, Oct 24 2011

Maple

a:=n->floor(2*n*sqrt(2)): seq(a(n),n=1..60); # Muniru A Asiru, Sep 28 2018

Mathematica

Table[Floor[2*n*Sqrt[2]], {n,1,60}] (* G. C. Greubel, Sep 28 2018 *)

PARI

vector(80, n, floor(2*n*sqrt(2))) \\ G. C. Greubel, Sep 28 2018

Python

from sympy import integer_nthroot
def A022842(n): return integer_nthroot(8*n**2,2)[0] # Chai Wah Wu, Mar 16 2021

Formula

a(n) = floor(2*n*sqrt(2)). - Michel Marcus, Oct 31 2017

Extensions

Offset changed from 0 to 1 by Vincenzo Librandi, Oct 24 2011