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

1,2

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

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

Mathematica

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

Prog

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

Crossrefs

Beatty complement is A059562.

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

Cf. A022932 (characteristic function).

Sequence in context: A179439 A047421 A004777 * A037474 A292638 A000378

Adjacent sequences: A059558 A059559 A059560 * A059562 A059563 A059564

Keyword

nonn,easy

Author

Mitch Harris, Jan 22 2001

Status

approved