Counting the numerical semigroups with a specific special gap

Abstract Let S be a numerical semigroup. An element is a special gap of S if is also a numerical semigroup. If a is a positive integer, we denote by the set of all numerical semigroups for which a is a special gap. We say that an element of is -irreducible if it cannot be expressed as the intersection of two numerical semigroups of properly containing it. The main aim of this paper is to describe three algorithmic procedures: the first one calculates the elements of the second one determines whether or not a numerical semigroup is -irreducible and the third one computes all the -irreducibles numerical semigroups.