A059535 Beatty sequence for Pi^2/6, or zeta(2).

1, 3, 4, 6, 8, 9, 11, 13, 14, 16, 18, 19, 21, 23, 24, 26, 27, 29, 31, 32, 34, 36, 37, 39, 41, 42, 44, 46, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 64, 65, 67, 69, 70, 72, 74, 75, 77, 78, 80, 82, 83, 85, 87, 88, 90, 92, 93, 95, 97, 98, 100, 101, 103, 105, 106, 108, 110, 111

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

Cf. A013661. Beatty complement is A059536.

Programs

Mathematica

Floor[Range[100]*Zeta[2]] (* Paolo Xausa, Jul 06 2024 *)

PARI

{ default(realprecision, 100); b=zeta(2); for (n = 1, 2000, write("b059535.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 27 2009

Formula

a(n) = floor(n*A013661). - Paolo Xausa, Jul 06 2024