We answer the Frobenius problem for a specific family of numerical semigroups with
embedding dimension 5. The numerical semigroups in this family are called fulcrum
numerical semigroups and are related to balanced and unitary numerical semigroups
introduced in earlier research. We show that fulcrum numerical semigroups come in
two distinct varieties and provide formulas for the Frobenius number and genus for
both.
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