Generalised Beatty sets

Marc Technau
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 2, Pages 127-135
DOI: 10.7546/nntdm.2019.25.2.127-135
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Authors and affiliations

Marc Technau
Institute of Analysis and Number Theory
Graz University of Technology, Kopernikusgasse 24, 8010 Graz, Austria

Abstract

Generalised Beatty sets, that is, sets of the form {⌊1 + 2 + β⌋ : m, n ∈ ℕ}, are studied, where ⌊ξ⌋ denotes the largest integer less than or equal to ξ. Such sets are shown to be contained in a suitable ordinary Beatty set {⌊ + β⌋ : n ∈ ℕ} and equal said set save for finitely many exceptions. Moreover, bounds for the largest such exception are given.

Keywords

  • Beatty sequence
  • Beatty set

2010 Mathematics Subject Classification

  • Primary: 11B83
  • Secondary: 11K60

References

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Cite this paper

APA

Technau, M.(2019). Generalised Beatty sets. Notes on Number Theory and Discrete Mathematics, 25(2), 127-135, doi: 10.7546/nntdm.2019.25.2.127-135.

Chicago

Technau, M. “Generalised Beatty sets.” Notes on Number Theory and Discrete Mathematics 25, no. 2 (2019): 127-135, doi: 10.7546/nntdm.2019.25.2.127-135.

MLA

Technau, M. “Generalised Beatty sets.” Notes on Number Theory and Discrete Mathematics 25.2 (2019): 127-135. Print, doi: 10.7546/nntdm.2019.25.2.127-135.

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