A075304 Smallest prime greater than the previous term == 1 mod n-th composite number.

5, 7, 17, 19, 31, 37, 43, 61, 97, 109, 181, 211, 331, 337, 401, 443, 487, 617, 631, 641, 661, 919, 1051, 1117, 1217, 1249, 1321, 1429, 1453, 1531, 1657, 1777, 2549, 2551, 2857, 2861, 2917, 2971, 3137, 3307, 3539, 3541, 3659, 3907, 4289, 4421, 4423, 5101