On the Numerical Semigroup Generated by {(2k − m) · 2n+i − 1|i ∈ ℕ}

Abstract

Let k, n be two positive integers such that 2 ≤ k ≤ 2n and m be an odd number with 1 ≤ m < 2k−1. Denote by T(k, m, n) a numerical semigroup generated by {(2k − m) · 2n+i − 1|i ∈ ℕ}. In this paper, we give the formula for the embedding dimension of T(k, m, n). In particular, the formulas for computing the Frobenius number and the genus of T(k, 2t + 1, n) with 2 ≤ t < k − 1 are given.