Bulletin of the
Korean Mathematical Society BKMS

The greatest integer that does not belong to a numerical semigroup $S$ is called the Frobenius number of $S$. The Frobenius problem, which is also called the coin problem or the money changing problem, is a mathematical problem of finding the Frobenius number. In this paper, we introduce the Frobenius problem for two kinds of numerical semigroups generated by the Thabit numbers of the first kind, and the second kind base $b$, and by the Cunningham numbers. We provide detailed proofs for the Thabit numbers of the second kind base $b$ and omit the proofs for the Thabit numbers of the first kind base $b$ and Cunningham numbers.

Keywords: Frobenius problem, Thabit numerical semigroups base $b$, Ap\'{e}ry set, genus, type

MSC numbers: Primary 11A67, 20M30

Supported by: This research was supported by the National Research Foundation of Korea grant funded by the Korea government (Grant Number: NRF2018R1A2A1A05079095).