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A158919

Beatty sequence for the tribonacci constant tau (A058265): a(n) = floor(n*tau).

0, 1, 3, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 23, 25, 27, 29, 31, 33, 34, 36, 38, 40, 42, 44, 45, 47, 49, 51, 53, 55, 57, 58, 60, 62, 64, 66, 68, 69, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 90, 91, 93, 95, 97, 99, 101, 103, 104, 106, 108, 110

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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

N. J. A. Sloane, Table of n, a(n) for n = 0..100000

A. J. Hildebrand, Junxian Li, Xiaomin Li, and 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.

Index entries for sequences related to Beatty sequences

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)) ;