A073125 a(n) is the least prime p(s) such that p(s+n)-p(s) is divisible by n, i.e. p(s+n)=kn+p(s).

2, 3, 17, 5, 17, 5, 13, 29, 2, 13, 17, 11, 7, 11, 7, 7, 11, 7, 7, 67, 5, 47, 193, 43, 3, 3, 5, 53, 173, 41, 181, 31, 181, 41, 211, 31, 211, 181, 113, 29, 173, 13, 173, 19, 229, 181, 197, 17, 193, 13, 113, 17, 113, 619, 191, 13, 179, 173, 167, 743, 1499, 7, 1627, 733