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arXiv · 2211.01436

The extended Frobenius problem for Lucas series incremented by a Lucas number

Aureliano M. Robles-Pérez·José Carlos Rosales
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Abstract

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.

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Aureliano M. Robles-Pérez, José Carlos Rosales. 2022-11-02. The extended Frobenius problem for Lucas series incremented by a Lucas number. https://doi.org/10.2989/16073606.2024.2422517

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