Distribution of odd and even elements in gap sets of numerical semigroups

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We observe the distribution of odd and even elements in the gap set of a numerical semigroup. For embedding dimension 2 or 3 and depending on the number of odd minimal generators of a numerical semigroup S, we compute O ( G ( S ) ) − E ( G ( S ) ) , the difference between the number of odd and even elements in the gap set. We also obtain the results on O ( G ( S ) ) − E ( G ( S ) ) when the minimal generators of S are one of the followings: some compound sequences, a geometric sequence, or an arithmetic sequence.