On $k$-Pell numbers that are Palindromes formed by two distinct Repdigits
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915251391299584 |
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| author | Batte, Herbert Guma, Darius |
| author_facet | Batte, Herbert Guma, Darius |
| contents | Let $k \ge 2$ and consider the sequence $\{P_n^{(k)}\}_{n \ge 2-k}$ of $k$-generalized Pell numbers, which begins with the first $k$ terms as $0, \ldots, 0, 0, 1$, and satisfies the recurrence relation $P_n^{(k)} = 2P_{n-1}^{(k)} + P_{n-2}^{(k)} + \cdots + P_{n-k}^{(k)}$ for all $n \ge 2$. In this work, we identify all terms in the $k$-Pell sequence that can be expressed as palindromes formed by concatenating two distinct repdigits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $k$-Pell numbers that are Palindromes formed by two distinct Repdigits Batte, Herbert Guma, Darius Number Theory 11B39, 11D61, 11D45 Let $k \ge 2$ and consider the sequence $\{P_n^{(k)}\}_{n \ge 2-k}$ of $k$-generalized Pell numbers, which begins with the first $k$ terms as $0, \ldots, 0, 0, 1$, and satisfies the recurrence relation $P_n^{(k)} = 2P_{n-1}^{(k)} + P_{n-2}^{(k)} + \cdots + P_{n-k}^{(k)}$ for all $n \ge 2$. In this work, we identify all terms in the $k$-Pell sequence that can be expressed as palindromes formed by concatenating two distinct repdigits. |
| title | On $k$-Pell numbers that are Palindromes formed by two distinct Repdigits |
| topic | Number Theory 11B39, 11D61, 11D45 |
| url | https://arxiv.org/abs/2504.14261 |