On Sylvester sums of compound sequence semigroup complements

In this paper, we consider the set NR(G) of natural numbers which are not in the numerical semigroup generated by a compound sequence G. We generalize a result of Tuenter which completely characterizes NR(G). We use this result to compute Sylvester sums, and we give a direct application to the computation of weights of higher-order Weierstrass points on some families of complex algebraic curves.