The Frobenius problem for the proth numbers

Let n be a positive integer greater than 2. We define \textit{the Proth numerical semigroup}, Pk(n), generated by {k2n+i+1?i?N}, where k is an odd positive number and k<2n. In this paper, we introduce the Frobenius problem for the Proth numerical semigroup Pk(n) and give formulas for the embedding dimension of Pk(n). We solve the Frobenius problem for Pk(n) by giving a closed formula for the Frobenius number. Moreover, we show that Pk(n) has an interesting property such as being Wilf.