Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture

The Huneke-Wiegand conjecture is a decades-long open question in commutative algebra. Garc\'ia-S\'anchez and Leamer showed that a special case of this conjecture concerning numerical semigroup rings can be answered in the affirmative by locating certain arithmetic sequences within the numerical semigroup. In this paper, we use their approach to prove the Huneke-Wiegand conjecture in the case where is generated by a generalized arithmetic sequence and showcase how visualizations can be leveraged to find the requisite arithmetic sequences.