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arXiv · 2409.06232

On the representation of an integer in Ostrowski and recurrence numeration systems

Mohit Mittal·Divyum Sharma
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Abstract

We provide an effective upper bound for positive integers with bounded Hamming weights with respect to both a linear recurrence numeration system and an Ostrowski-$\alpha$ numeration system, where $\alpha$ is a quadratic irrational. We prove a similar result for the representation of an integer in two \textit{different} Ostrowski numeration systems.

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Mohit Mittal, Divyum Sharma. 2024-09-10. On the representation of an integer in Ostrowski and recurrence numeration systems. https://arxiv.org/abs/2409.06232

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