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arXiv · 2507.00317

Fixed Points of the Josephus Function via Fractional Base Expansions

Yunier Bello-Cruz·Roy Quintero-Contreras
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Abstract

In this paper, we investigate properties of the fixed point sequence of the Josephus function $J_3$. First, we establish a connection between this sequence and the Chinese Remainder Theorem. Next, we identify a clear numerical pattern for the digits of two consecutive fixed points when they are written in a non-standard fractional number system in base $3/2$. This result enables us to derive a recursive procedure for determining the digits of their base $3/2$ expansions.

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Yunier Bello-Cruz, Roy Quintero-Contreras. 2025-06-30. Fixed Points of the Josephus Function via Fractional Base Expansions. https://arxiv.org/abs/2507.00317

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