BALKAN 1988 Problem 4

Let $(a_{n})_{n\geq 1}$ be a sequence defined by $a_{n}=2^{n}+49$ . Find all values of $n$ such that $a_{n}=pg, a_{n+1}=rs$ , where $p,q,r,s$ are prime numbers with $p<q, r<s$ and $q-p=s-r$ .