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

**Full paper (PDF, 196 Kb)**

## Details

### 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 {⌊*mα*_{1} + *nα*_{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 {⌊*nα* + *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

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.