How long can $k$-Göbel sequences remain integers?
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909556415660032 |
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| author | Matsuhira, Rinnosuke Matsusaka, Toshiki Tsuchida, Koki |
| author_facet | Matsuhira, Rinnosuke Matsusaka, Toshiki Tsuchida, Koki |
| contents | Inspired by Episode 3 of the Japanese manga "Seisu-tan" by Doom Kobayashi and Shin-ichiro Seki, we investigate the $k$-Göbel sequence $(g_{k,n})_n$ named after Fritz Göbel. Although the sequence is generally defined as rational, quite a few initial terms behave like an integer sequence. This article addresses a question raised in Seisu-tan and shows that $g_{k,n}$ is always an integer for any $k \geq 2$ and $0 \leq n \leq 18$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09741 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | How long can $k$-Göbel sequences remain integers? Matsuhira, Rinnosuke Matsusaka, Toshiki Tsuchida, Koki Number Theory Combinatorics 11B37, 11B50 Inspired by Episode 3 of the Japanese manga "Seisu-tan" by Doom Kobayashi and Shin-ichiro Seki, we investigate the $k$-Göbel sequence $(g_{k,n})_n$ named after Fritz Göbel. Although the sequence is generally defined as rational, quite a few initial terms behave like an integer sequence. This article addresses a question raised in Seisu-tan and shows that $g_{k,n}$ is always an integer for any $k \geq 2$ and $0 \leq n \leq 18$. |
| title | How long can $k$-Göbel sequences remain integers? |
| topic | Number Theory Combinatorics 11B37, 11B50 |
| url | https://arxiv.org/abs/2307.09741 |