On the Frobenius number of certain numerical semigroups

Abstract

Let [Formula: see text], [Formula: see text], be a real and [Formula: see text] a prime number, with [Formula: see text] containing at least two primes. Denote by [Formula: see text] the largest integer which cannot be written as a sum of primes from [Formula: see text]. Then [Formula: see text] Further a question of Wilf about the “Money-Changing Problem” has a positive answer for all semigroups of multiplicity [Formula: see text] containing the primes from [Formula: see text]. In particular, this holds for the semigroup generated by all primes not less than [Formula: see text]. The latter special case was already shown in a previous paper.