Consider the set $\{0, 3, 7, 15\}$ of four integers. If you add each of these numbers to a fixed power of 2, then the resulting four numbers are pairwise coprime. For example, $\{4, 7, 11, 19\}$ are pairwise coprime, as are $\{32, 35, 39, 47\}$. I can construct similar sets of any finite size, and for any prime.
Is there a name for such sets or any literature about sets with this property? Thanks for any references!
