The Frobenius Problem for Generalized Repunit Numerical Semigroups

Abstract In this paper, we introduce and study the numerical semigroups generated by $$\{a_1, a_2, \ldots \} \subset {\mathbb {N}}$$ { a 1 , 2 … } ⊂ N such that $$a_1$$ is repunit number in base $$b > 1$$ b > of length $$n n $$a_i - a_{i-1} = a\, b^{i-2},$$ i - = for every $$i \ge 2$$ ≥ , where a positive integer relatively prime with . These generalize among many others. We show they have interesting properties as being homogeneous Wilf. Moreover, solve Frobenius problem family, giving closed formula terms b n compute other usual invariants Apéry sets, genus or type.