A New Algorithm for Computing the Frobenius Number

A number $\alpha$ has a representation with respect to the numbers $\alpha_1,...,\alpha_n$, if there exist the non-negativeintegers $\lambda_1,... ,\lambda_n$ such that $\alpha=\lambda_1\alpha_1+...+\lambda_n \alpha_n$. The largest natural number that does not have a representation with respect to the numbers $\alpha_1,...,\alpha_n$ is called the Frobenius number and is denoted by the symbol$g(\alpha_1,...,\alpha_n)$. In this paper, we present a new algorithm to calculate the Frobenius number. Also we present the sequential form of the new algorithm. A number $\alpha$ has a representation with respect to the numbers $\alpha_1,...,\alpha_n$, if there exist the non-negativeintegers $\lambda_1,... ,\lambda_n$ such that $\alpha=\lambda_1\alpha_1+...+\lambda_n \alpha_n$.The largest natural number that does not have a representation with respect to the numbers $\alpha_1,...,\alpha_n$ is called theFrobenius number and is denoted by the symbol $g(\alpha_1,...,\alpha_n)$. In this paper, we present a new algorithm to calculate theFrobenius number. Also we present the sequential form of the new algorithm.