THE FROBENIUS PROBLEM FOR REPUNIT NUMERICAL SEMIGROUPS

Abstract

A repunit is a number consisting of copies of the single digit 1. The set of repunits in base b is { bn􀀀1 b􀀀1 j n 2 Nnf0g } . A numerical semigroup S is a repunit numerical semigroup if there exist integers b 2 Nn f0; 1g and n 2 Nn f0g such that S = ⟨{ bn+i􀀀1 b􀀀1 j i 2 N }⟩ . In this work, we give formulas for the embedding dimension, the Frobenius number, the type and the genus for a repunit numerical semigroup.