English

The extended Frobenius problem for Fibonacci sequences incremented by a Fibonacci number

Number Theory 2023-05-29 v2 Combinatorics

Abstract

We study the extended Frobenius problem for sequences of the form {fa+fn}nN\{f_a+f_n\}_{n\in\mathbb{N}}, where {fn}nN\{f_n\}_{n\in\mathbb{N}} is the Fibonacci sequence and faf_a is a Fibonacci number. As a consequence, we show that the family of numerical semigroups associated to these sequences satisfies the Wilf's conjecture.

Keywords

Cite

@article{arxiv.2210.00816,
  title  = {The extended Frobenius problem for Fibonacci sequences incremented by a Fibonacci number},
  author = {Aureliano M. Robles-Pérez and José Carlos Rosales},
  journal= {arXiv preprint arXiv:2210.00816},
  year   = {2023}
}

Comments

11 pages; typos corrected

R2 v1 2026-06-28T02:35:35.080Z