A059561 Beatty sequence for log(Pi).

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81

Offset: 1

Author

Mitch Harris, Jan 22 2001

Keywords

• nonn
• easy

Comments

a(n) is the largest integer m such that e^m < Pi^n. - Stanislav Sykora, May 29 2015

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 A059562.

Cf. A000796 (Pi), A001113 (e), A053510 (log(Pi)).

Cf. A022932 (characteristic function).

Programs

Mathematica

Floor[Range[100]*Log[Pi]] (* Paolo Xausa, Jul 05 2024 *)

PARI

{ default(realprecision, 100); b=log(Pi); for (n = 1, 2000, write("b059561.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009

Formula

a(n) = A004777(n+1), 1 <= n < 83. - R. J. Mathar, Oct 05 2008

a(n) = floor(n*log(Pi)). - Michel Marcus, Jan 04 2015