In this paper, we consider the set $\textit{ NR}(G)$ 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 $\textit{ NR}(G)$. 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.
Categories: math.NT