OFFSET
0,3
COMMENTS
Also called the spectrum of tau. Note that A276384 agrees with this sequence for n <= 17160 but disagrees beyond that point. In fact a(17161) = 31564, whereas A276384(17161) = 31563. - N. J. A. Sloane, Sep 03 2016
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..20000
A. J. Hildebrand, Junxian Li, Xiaomin Li, Yun Xie, Almost Beatty Partitions, arXiv:1809.08690 [math.NT], 2018.
Wolfdieter Lang, The Tribonacci and ABC Representations of Numbers are Equivalent, arXiv preprint arXiv:1810.09787 [math.NT], 2018.
N. J. A. Sloane, Table of n, a(n) for n = 0..100000
FORMULA
a(n) = floor(n*A058265).
EXAMPLE
a(3) = floor(3*q) = floor(3*1.8392867...) = floor(5.51786...) = 5.
MAPLE
x := (1/3)*(1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3)) ;
[seq(floor(n*x), n=0..200)]; # R. J. Mathar, Sep 11 2011
MATHEMATICA
a[n_] := Floor[n Root[#^3 - #^2 - # - 1&, 1]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 28 2018 *)
PROG
(Magma) [Floor(n * (1/3 + 1/3 * (19 - 3 * Sqrt(33))^(1/3) + 1/3 * (19 + 3 * Sqrt(33))^(1/3))) : n in [0..80]]; // Vincenzo Librandi, Oct 28 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Culver (weux082690(AT)yahoo.com), Mar 30 2009
STATUS
approved