A Note on Iterated Beatty Sequences

Mohsen Khani; Ali N. Valizadeh; Afshin Zarei

A Note on Iterated Beatty Sequences

Number Theory 2026-07-14 v1

Authors: Mohsen Khani , Ali N. Valizadeh , Afshin Zarei

Abstract

For any irrational number $\alpha>\frac{3+\sqrt{5}}{2}\approx2.618$ and given a positive $n\in\mathbb{N}$ , we use elementary number theory to introduce a necessary and sufficient condition for a natural number $x$ to be in the $n$ th iterate of the Beatty sequence of modulus $\alpha$ .

Cite

@article{arxiv.2607.12817,
  title  = {A Note on Iterated Beatty Sequences},
  author = {Mohsen Khani and Ali N. Valizadeh and Afshin Zarei},
  journal= {arXiv preprint arXiv:2607.12817},
  year   = {2026}
}

Comments

10 pages