  In this work we present a new class of numerical semigroups called
GSI-semigroups. We see the relations between them and others families of
semigroups and we give explicitly their set of gaps. Moreover, an algorithm to
obtain all the GSI-semigroups up to a given Frobenius number is provided and
the realization of positive integers as Frobenius numbers of GSI-semigroups is
studied.
