On the length over which $k$-Göbel sequences remain integers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910843080278016 |
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| author | Kobayashi, Yuh Seki, Shin-ichiro |
| author_facet | Kobayashi, Yuh Seki, Shin-ichiro |
| contents | We prove that the sequence $(N_k)_k$, where each $N_k$ is defined as the smallest positive integer $n$ for which the $n$th term $g_{k,n}$ of the $k$-Göbel sequence is not an integer, is unbounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the length over which $k$-Göbel sequences remain integers Kobayashi, Yuh Seki, Shin-ichiro Combinatorics 11B37, 11B50 We prove that the sequence $(N_k)_k$, where each $N_k$ is defined as the smallest positive integer $n$ for which the $n$th term $g_{k,n}$ of the $k$-Göbel sequence is not an integer, is unbounded. |
| title | On the length over which $k$-Göbel sequences remain integers |
| topic | Combinatorics 11B37, 11B50 |
| url | https://arxiv.org/abs/2502.17448 |