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A059561
Beatty sequence for log(Pi).
6
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
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.
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
KEYWORD
nonn,easy
AUTHOR
Mitch Harris, Jan 22 2001
STATUS
approved