A059537 -id:A059537 - cp's OEIS frontend

A059538 Beatty sequence for zeta(3)/(zeta(3)-1).

5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95, 101, 107, 113, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 237, 243, 249, 255, 261, 267, 273, 279, 285, 291, 297, 303, 309, 315, 321, 327

Offset: 1

Mitch Harris, Jan 22 2001

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

Cf. A002117. Beatty complement is A059537.

Floor[Range[100]*(1 + 1/(Zeta[3] - 1))] (* Paolo Xausa, Jul 08 2024 *)

{ default(realprecision, 100); b=zeta(3)/(zeta(3) - 1); for (n = 1, 2000, write("b059538.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 27 2009

a(n) = floor(n*zeta(3)/(zeta(3)-1)). - Michel Marcus, Jan 05 2015

A372767 Decimal expansion of Sum_{k >= 1} floor(k*zeta(3))/2^k.

Original entry on oeis.org

2, 0, 6, 4, 5, 1, 6, 1, 2, 9, 0, 3, 2, 2, 5, 8, 0, 6, 4, 5, 1, 6, 1, 2, 9, 0, 3, 2, 2, 5, 9, 6, 9, 3, 1, 3, 2, 1, 9, 1, 4, 2, 4, 0, 2, 4, 3, 7, 2, 4, 6, 2, 9, 2, 3, 4, 8, 9, 6, 1, 8, 6, 4, 4, 2, 9, 9, 8, 2, 7, 1, 5, 5, 9, 5, 0, 3, 4, 9, 3, 1, 9, 8, 8, 1, 4, 5, 7, 7, 5

Offset: 1

Paolo Xausa, May 12 2024

			2.0645161290322580645161290322596931321914240243724629234896...

Paolo Xausa, Table of n, a(n) for n = 1..10000
J. M. Borwein and P. B. Borwein, Strange Series and High Precision Fraud, The American Mathematical Monthly, Vol. 99, No. 7 (1992), pp. 622-640.

Cf. A000079, A002117, A059537, A372610, A372766.

First[RealDigits[Sum[Floor[k*Zeta[3]]/2^k, {k, 350}], 10, 100]]

Equals Sum_{k >= 1} A059537(k)/A000079(k).

Approximately 64/31, correct to 30 digits: see Example 4.1 in Borwein and Borwein (1992), p. 634.

cp's OEIS Frontend

A059538 Beatty sequence for zeta(3)/(zeta(3)-1).

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