A059558 Beatty sequence for 1 + 1/gamma^2.

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228

Offset: 1

Author

Mitch Harris, Jan 22 2001

Keywords

• nonn
• easy

Comments

The first term where this sequence breaks the progression a(n) = a(n-1) + 4 is a(715) = 2861. - Max Alekseyev, Mar 03 2007

Links

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

Crossrefs

Beatty complement is A059557.

Cf. A001620, A098907, A155969.

Programs

Mathematica

Floor[Range[100]*(1 + 1/EulerGamma^2)] (* Paolo Xausa, Jul 05 2024 *)

PARI

{ default(realprecision, 100); b=1 + 1/Euler^2; for (n = 1, 2000, write("b059558.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009

Formula

a(n) = floor(n*(1+1/gamma^2)) where 1+1/gamma^2= 1+A098907^2 = 4.00139933... - R. J. Mathar, Sep 29 2023

Extensions

Removed incorrect comment, Joerg Arndt, Nov 14 2014