Beurling generalized integers with the Delone Property

A set N of Beurling generalized integers consists of the unit n(0) = 1 plus the set n(1) less than or equal to n(2) less than or equal to ... of all power products of a set of generalized primes 1 infinity, with these power products arranged in increasing order and counted with multiplicity. We say that N has the Delone property if there are positive constants r, R such that R greater than or equal to n(i + 1) - n(i) greater than or equal to r for all i greater than or equal to 1. Any set N with the Delone property has unique factorization into irreducible elements and is therefore a subsemigroup of R+. We classify all such semigroups which are contained in the integers Z(+). The set of generalized primes of any such N consists of all but finitely many primes, plus finitely many other composites.