A numerical semigroup S is a subset of the set of nonnegative integers closed under addition, containing the zero element and with finite complement in \({\mathbb {N}}_{0}\) (this finite cardinality is named the genus of S). It is well-known that every numerical semigroup S is finitely generated and there are many works concerning the properties of numerical semigroups with a particular type of generators. For instance, Song (Bull Korean Math Soc 57:623–647, 2020) worked on these semigroups whose generators are Thabit numbers of the first, second kind base b and Cunningham numbers. A classical result of Sylvester ensures that if \(\gcd (a,b) = 1\), then the numerical semigroup \(\langle a, b \rangle \) has genus \(\frac{(a-1)(b-1)}{2}\). In this paper, we search for two-generator numerical semigroups whose generators and/or the genus are related to Fibonacci numbers. Our propose is fixing the sets A, B and G and looking for triples \((a, b, g) \in A\times B\times G\), where at least one of the sets is related to the Fibonacci numbers.

数值半群S是在加法下闭合的非负整数集合的子集，包含零元素和在\({\mathbb {N}}_{0}\) 中的有限补（这个有限基数被命名为小号）。众所周知，每个数值半群S都是有限生成的，并且有许多关于具有特定类型生成器的数值半群的性质的工作。例如，Song (Bull Korean Math Soc 57:623–647, 2020) 研究了这些半群，其生成元是第一类、第二类基数b 的Thabit 数和 Cunningham 数。Sylvester 的经典结果确保如果\(\gcd (a,b) = 1\)，则数值半群\(\langle a, b \rangle \)有属\(\frac{(a-1)(b-1)}{2}\)。在本文中，我们搜索其生成元和/或属与斐波那契数相关的双生成元数值半群。我们的提议是修复集合A、  B和G并寻找三元组\((a, b, g) \in A\times B\times G\)，其中至少一组与斐波那契数列相关。