• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.455-460
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• 2004

Let $S_{i}$ be the numerical semigroup generated by the set ${a,\;a{\;}+{\;}d,{\cdots},\;a+(i{\;}-{\;}l)d,\;a+(i{\;}+{\;}l)d,{\cdots},{\;}a{\;}+{\;}rd}$. In this paper, we will formulate the number of nonmembers of each set $S_{i}$ and find the if and only if conditions under which $S_1$ and $S_{r-1}$ are symmetric.