The extended Frobenius problem for Lucas series incremented by a Lucas number
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| author | Robles-Pérez, Aureliano M. Rosales, José Carlos |
| author_facet | Robles-Pérez, Aureliano M. Rosales, José Carlos |
| contents | We study the extended Frobenius problem for sequences of the form $\{l_a\}\cup\{l_a+l_n\}_{n\in\mathbb{N}}$ and $\{l_a+l_n\}_{n\in\mathbb{N}}$, where $\{l_n\}_{n\in\mathbb{N}}$ is the Lucas series and $l_a$ is a Lucas number. As a consequence, we show that the families of numerical semigroups associated to both sequences satisfy the Wilf's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01436 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The extended Frobenius problem for Lucas series incremented by a Lucas number Robles-Pérez, Aureliano M. Rosales, José Carlos Number Theory 11D07, 11B39 (Primary), 11A67, 05A17 (Secondary) We study the extended Frobenius problem for sequences of the form $\{l_a\}\cup\{l_a+l_n\}_{n\in\mathbb{N}}$ and $\{l_a+l_n\}_{n\in\mathbb{N}}$, where $\{l_n\}_{n\in\mathbb{N}}$ is the Lucas series and $l_a$ is a Lucas number. As a consequence, we show that the families of numerical semigroups associated to both sequences satisfy the Wilf's conjecture. |
| title | The extended Frobenius problem for Lucas series incremented by a Lucas number |
| topic | Number Theory 11D07, 11B39 (Primary), 11A67, 05A17 (Secondary) |
| url | https://arxiv.org/abs/2211.01436 |