Dense numerical semigroups

A numerical semigroup S is dense if for all $$s\in S\backslash \{0\}$$ we have $$\left\{ s-1,s+1\right\} \cap S\ne \emptyset $$ . We give algorithms to compute the whole set of dense numerical semigroups with fixed genus, Frobenius number and multiplicity. Furthermore, we solve the Frobenius problem for dense numerical semigroups with embedding dimension three.