The number system in rational base $3/2$ and the $3x+1$ problem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916696255627264 |
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| author | Eliahou, Shalom Verger-Gaugry, Jean-Louis |
| author_facet | Eliahou, Shalom Verger-Gaugry, Jean-Louis |
| contents | The representation of numbers in rational base $p/q$ was introduced in 2008 by Akiyama, Frougny & Sakarovitch, with a special focus on the case $p/q=3/2$. Unnoticed since then, natural questions related to representations in that specific base turn out to intimately involve the Collatz $3x+1$ function. Our purpose in this note is to expose these links and motivate further research into them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The number system in rational base $3/2$ and the $3x+1$ problem Eliahou, Shalom Verger-Gaugry, Jean-Louis Number Theory 11B83, 68R15 The representation of numbers in rational base $p/q$ was introduced in 2008 by Akiyama, Frougny & Sakarovitch, with a special focus on the case $p/q=3/2$. Unnoticed since then, natural questions related to representations in that specific base turn out to intimately involve the Collatz $3x+1$ function. Our purpose in this note is to expose these links and motivate further research into them. |
| title | The number system in rational base $3/2$ and the $3x+1$ problem |
| topic | Number Theory 11B83, 68R15 |
| url | https://arxiv.org/abs/2504.13716 |