Research Article

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

Published in: Quaestiones Mathematicae
Volume 48 , issue 4 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 703–716
DOI: 10.2989/16073606.2024.2422517
Author(s): Aureliano M. Robles-Pérez Universidad de Granada, Spain, José Carlos Rosales Universidad de Granada, Spain,
Keywords: Primary: 11D07, 11B39, Secondary: 11A67, 05A17, Lucas numbers, Lucas series, Frobenius problem, numerical semigroup, Apéry set, Frobenius number, genus, Wilf ’s conjecture,
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Abstract

We study the extended Frobenius problem for sequences of the form {la } ∪ {la + ln } n∈N and {la + ln } n ∈N , where {ln } n∈N is the Lucas series and la 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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