A059559 Beatty sequence for 1 + log(1/gamma), (gamma is the Euler-Mascheroni constant A001620).
1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 96, 97, 99, 100, 102, 103, 105, 106
Offset: 1
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 A059560.
Programs
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Magma
R:=RealField(100); [Floor(1+Log(1/EulerGamma(R))*n): n in [1..100]]; // G. C. Greubel, Aug 27 2018
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Mathematica
Table[Floor[n*(1 + Log[1/EulerGamma])], {n,1,100}] (* G. C. Greubel, Aug 27 2018 *) -
PARI
{ default(realprecision, 100); b=1 + log(1/Euler); for (n = 1, 2000, write("b059559.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009
Formula
a(n) = floor(n*(1 + log(1/Euler))). - Michel Marcus, Jan 05 2015
Extensions
Corrected the definition from 1-log(1/gamma) to 1+log(1/gamma). - Harry J. Smith, Jun 28 2009