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a b s t r a c tWe investigate the weights of a family of numerical semigroups by means of even gaps and the Weierstrass property for such a family.

Abstract. Given a positive integer κ, we investigate the class of numerical semigroups verifying the property that every two subsequent non gaps, smaller than the conductor, are spaced by at least κ. These semigroups will be called κ-sparse and generalize the concept of sparse numerical semigroups.

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