All Triply Telescopic Numerical Semigroups with Multiplicity 12

Numerical semigroups form a subset of non-negative integers. Of these semigroups, symmetric ones have an important place. It is of particular importance to examine and classify telescopic numerical semigroups, which form a class of symmetric numerical semigroups. Especially finding their Frobenius numbers and spaces is a problem in itself. In this study, we will examine some telescopic numerical semigroups that will contribute to the solution to this problem. Here we will characterize all telescopic numerical semigroups produced by three elements with multiplicity 12. We will also give formulas to calculate the genus, determine number and Frobenius number in these semigroups.