Frobenius number and minimal presentation of certain numerical semigroups

Suppose e?4 be an integer, a=e+1, b>a+(e?3)d, gcd(a,d)=1 and d?(b?a). Let M={a,a+d,a+2d,�,a+(e?3)d,b,b+d}, which forms a minimal generating set for the numerical semigroup ?e(M), generated by the set M. We calculate the Ap\'{e}ry set and the Frobenius number of ?e(M). We also show that the minimal number of generators for the defining ideal p of the affine monomial curve parametrized by X0=ta, X1=ta+d,�,Xe?3=ta+(e?3)d, Xe?2=tb, Xe?1=tb+d is a bounded function of e.