A Frobenius problem suggested by prime $k$-tuplets (extended version)

TL;DR

This paper investigates the Frobenius problem for specific k-tuplets, including prime k-tuplets like triplets and quadruplets, and explores related properties of their numerical semigroups.

Contribution

It introduces a new approach to the Frobenius problem for prime k-tuplets and analyzes their associated numerical semigroups, extending existing theories.

Findings

Derived Frobenius numbers for certain prime k-tuplets

Identified properties of numerical semigroups related to these tuplets

Extended the understanding of Frobenius problems in the context of prime configurations

Abstract

We study the Frobenius problem for certain k-tuplets, which include prime k-tuplets, in particular prime triplets and prime quadruplets. Moreover, we analyze some properties of the numerical semigroups associated with these tuplets.