A059543 Beatty sequence for log(3).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96

Offset: 1

Author

Mitch Harris, Jan 22 2001

Keywords

• nonn
• easy

Comments

Differs from A160542 at indices n=81, 91, 101, 111, 121, 131, 141, 151, 152, 161 etc. - R. J. Mathar, May 20 2009

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 A059544.

Cf. A002391 (log(3)).

Cf. A160542.

Programs

Maple

A059543 := proc(n)
    floor(n*log(3)) ;
end proc:
seq(A059543(n),n=1..100) ; # R. J. Mathar, Jun 26 2023

Mathematica

Floor[Range[100]*Log[3]] (* Paolo Xausa, Jul 05 2024 *)

PARI

{ default(realprecision, 100); b=log(3); for (n = 1, 2000, write("b059543.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009

Formula

a(n) = floor(n*A002391). - Paolo Xausa, Jul 05 2024