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arXiv · 2607.12817

A Note on Iterated Beatty Sequences

Mohsen Khani·Ali N. Valizadeh·Afshin Zarei
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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 $\alpha$.

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Mohsen Khani, Ali N. Valizadeh, Afshin Zarei. 2026-07-14. A Note on Iterated Beatty Sequences. https://arxiv.org/abs/2607.12817

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