On Palindromic forms in the $k$-Lucas sequence composed of two distinct Repdigits
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908377906413568 |
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| author | Batte, Herbert Kaggwa, Prosper |
| author_facet | Batte, Herbert Kaggwa, Prosper |
| contents | For integers $k \geq 2$, the $k$-generalized Lucas sequence $\{L_n^{(k)}\}_{n \geq 2-k}$ is defined by the recurrence relation \[ L_n^{(k)} = L_{n-1}^{(k)} + \cdots + L_{n-k}^{(k)} \quad \text{for } n \geq 2, \] with initial terms given by $L_0^{(k)} = 2$, $L_1^{(k)} = 1$, and $L_{2-k}^{(k)} = \cdots = L_{-1}^{(k)} = 0$. In this paper, we extend work in \cite{Lucas} and show that the result in \cite{Lucas} still holds for $k\ge 3$, that is, we show that for $k\ge 3$, there is no $k$-generalized Lucas number appearing as a palindrome formed by concatenating two distinct repdigits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Palindromic forms in the $k$-Lucas sequence composed of two distinct Repdigits Batte, Herbert Kaggwa, Prosper General Mathematics 11B39, 11D61, 11D45, 11Y50 For integers $k \geq 2$, the $k$-generalized Lucas sequence $\{L_n^{(k)}\}_{n \geq 2-k}$ is defined by the recurrence relation \[ L_n^{(k)} = L_{n-1}^{(k)} + \cdots + L_{n-k}^{(k)} \quad \text{for } n \geq 2, \] with initial terms given by $L_0^{(k)} = 2$, $L_1^{(k)} = 1$, and $L_{2-k}^{(k)} = \cdots = L_{-1}^{(k)} = 0$. In this paper, we extend work in \cite{Lucas} and show that the result in \cite{Lucas} still holds for $k\ge 3$, that is, we show that for $k\ge 3$, there is no $k$-generalized Lucas number appearing as a palindrome formed by concatenating two distinct repdigits. |
| title | On Palindromic forms in the $k$-Lucas sequence composed of two distinct Repdigits |
| topic | General Mathematics 11B39, 11D61, 11D45, 11Y50 |
| url | https://arxiv.org/abs/2505.09638 |