Beatty sequence

The integer sequence

$$ℬ(\alpha ,{\alpha }^{\prime }):={\left(\lfloor \frac{n-{\alpha }^{\prime }}{\alpha }\rfloor \right)}_{n=1}^{\mathrm{\infty }}$$

is called the Beatty sequence with density $\alpha$, slope $\frac{1}{\alpha }$, offset ${\alpha }^{\prime }$, and $y$-intercept $\frac{-{\alpha }^{\prime }}{\alpha }$.

Sometimes a sequence of the above type is called a floor Beatty sequence, and denoted ${ℬ}^{(f)}(\alpha ,{\alpha }^{\prime })$, while an integer sequence

$${ℬ}^{(c)}(\alpha ,{\alpha }^{\prime }):={\left(\lceil \frac{n-{\alpha }^{\prime }}{\alpha }\rceil \right)}_{n=1}^{\mathrm{\infty }}$$

is called a ceiling Beatty sequence.

References

[1

] M. Lothaire, , vol. 90, Cambridge University Press, Cambridge, 2002, ISBN 0-521-81220-8, available online at http://www-igm.univ-mlv.fr/~berstel/Lothaire. A collective work by Jean Berstel, Dominique Perrin, Patrice Seebold, Julien Cassaigne, Aldo De Luca, Steffano Varricchio, Alain Lascoux, Bernard Leclerc, Jean-Yves Thibon, Veronique Bruyere, Christiane Frougny, Filippo Mignosi, Antonio Restivo, Christophe Reutenauer, Dominique Foata, Guo-Niu Han, Jacques Desarmenien, Volker Diekert, Tero Harju, Juhani Karhumaki and Wojciech Plandowski; With a preface by Berstel and Perrin. http://www.ams.org/mathscinet-getitem?mr=1905123MR 1905123

Title	Beatty sequence
Canonical name	BeattySequence
Date of creation	2013-03-22 13:37:23
Last modified on	2013-03-22 13:37:23
Owner	Kevin OBryant (1315)
Last modified by	Kevin OBryant (1315)
Numerical id	12
Author	Kevin OBryant (1315)
Entry type	Definition
Classification	msc 11B83
Related topic	BeattysTheorem
Related topic	FraenkelsPartitionTheorem
Related topic	DataStream
Related topic	WideraInterlaceAndDeinterlace