A059563 Beatty sequence for e + 1/e.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175, 178, 182, 185

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 A059564.

Cf. A137204 (e+1/e).

Programs

Mathematica

Floor[Range[100]*(E + 1/E)] (* Paolo Xausa, Jul 06 2024 *)

PARI

{ default(realprecision, 100); b=exp(1) + 1/exp(1); for (n = 1, 2000, write("b059563.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009

Formula

a(n) = floor(n*(e+1/e)). - Michel Marcus, Jan 04 2015