OPEN

Let $k\leq n$. What choice of $A\subseteq \{1,\ldots,n\}$ of size $\lvert A\rvert=k$ maximises the number of integers not representable as the sum of finitely many elements from $A$ (with repetitions allowed)? Is it $\{n,n-1,\ldots,n-k+1\}$?

Associated with problems of Frobenius.