The <i>p</i>-Frobenius Number for the Triple of the Generalized Star Numbers

Abstract

In this paper, we give closed-form expressions of the p-Frobenius number for the triple of the generalized star numbers an(n−1)+1 for an integer a≥4. When a=6, it is reduced to the famous star number. For the set of given positive integers {a1,a2,…,ak}, the p-Frobenius number is the largest integer N whose number of non-negative integer representations N=a1x1+a2x2+⋯+akxk is at most p. When p=0, the 0-Frobenius number is the classical Frobenius number, which is the central topic of the famous linear Diophantine problem of Frobenius.

Keywords

• Frobenius problem
• Frobenius numbers
• centered 2a-gonal numbers
• the number of representations