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arXiv · 2211.08374

On the length of Pierce expansions

Zachary Chase·Mayank Pandey
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Abstract

For a given positive integer $n$, how long can the process $x \mapsto n\text{ }(\text{mod } x)$ last before reaching $0$? We improve Erd\H{o}s and Shallit's upper bound of $O(n^{\frac{1}{3}+\varepsilon})$ to $O(n^{\frac{1}{3}-\frac{2}{177}+\varepsilon})$ for any $\varepsilon > 0$.

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Zachary Chase, Mayank Pandey. 2022-11-15. On the length of Pierce expansions. https://arxiv.org/abs/2211.08374

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