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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.00317 |
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| _version_ | 1866908871056949248 |
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| author | Bello-Cruz, Yunier Quintero-Contreras, Roy |
| author_facet | Bello-Cruz, Yunier Quintero-Contreras, Roy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed Points of the Josephus Function via Fractional Base Expansions Bello-Cruz, Yunier Quintero-Contreras, Roy General Mathematics 11B37 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. |
| title | Fixed Points of the Josephus Function via Fractional Base Expansions |
| topic | General Mathematics 11B37 |
| url | https://arxiv.org/abs/2507.00317 |