On consecutive subset sums Original Research Article

We consider the subset sums analog of the linear Diophantine problem of Frobenius. It is shown that if A ⊑ [1;l] is a sufficiently dense set of n positive integers, then [2l − 2n + 1; σ − (2l − 2n + 1)] ⊑ A*, where σ is the sum of all elements of A, and A* is the set of all subset sums of A. The interval above is best possible and cannot be extended.