The Frobenius problem for repunit numerical semigroups

A repunit is a number consisting of copies of the single digit 1. The set of repunits in base b is (big {frac{b^n-1}{b-1} ~|~ nin {mathbb N}backslash {0}big }). A numerical semigroup S is a repunit numerical semigroup if there exist integers (bin {mathbb N}backslash left{ 0,1right} ) and (nin {mathbb N}backslash left{ 0right} ) such that (S=big langle big {frac{b^{n+i}-1}{b-1} ~|~ iin {mathbb N}big }big rangle ). In this work, we give formulas for the embedding dimension, the Frobenius number, the type and the genus for a repunit numerical semigroup.