A059564 Beatty sequence for (e^2 + 1)/(e^2 - e + 1).

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 73, 75, 76, 78, 79, 81, 82, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 99, 100, 102, 103

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, 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 A059563.

Programs

Maple

A059564:=n->floor(n*(exp(1)^2+1)/(exp(1)^2-exp(1)+1)): seq(A059564(n), n=1..100); # Wesley Ivan Hurt, Jan 03 2016

Mathematica

Table[Floor[n (E^2 + 1)/(E^2 - E + 1)], {n, 80}] (* Wesley Ivan Hurt, Jan 03 2016 *)

PARI

{ default(realprecision, 100); e=exp(1); b=(e^2 + 1)/(e^2 - e + 1); for (n = 1, 2000, write("b059564.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009

Formula

a(n) = floor(n*(e^2+1)/(e^2-e+1)). - Michel Marcus, Jan 05 2015