On the Frobenius number of certain numerical semigroups

Let $0<\lambda \le 1$, $\lambda\notin\left{\frac24, \frac27, \frac2{10}, \frac2{13}, \ldots\right}$,bearealand$p$aprimenumber,with$[p,p+\lambda p]$containingatleasttwoprimes\mathrm{.}Denoteby$f_\lambda(p)$ the largest integer which cannot be written as a sum of primes from $[p,p+\lambda p]$. Then $$f_{\lambda }(p)\sim \lfloor 2+\frac{2}{\lambda }\rfloor \cdot p\text{, as }p\text{ goes to infinity.}$$ Further a question of Wilf about the ‘Money-Changing Problem’ has a positive answer for all semigroups of multiplicity $p$ containing the primes from $[p,2p]$. In particular, this holds for the semigroup generated by all primes not less than $p$. The latter special case was already shown in a previous paper.