A101595 a(1) = 2; a(n+1) is the least prime p not already used such that p-a(n) is not equal to a(k+1)-a(k) for any k < n.

2, 3, 5, 11, 7, 17, 29, 13, 31, 19, 23, 37, 53, 43, 41, 61, 47, 71, 79, 59, 89, 67, 101, 73, 109, 83, 127, 97, 137, 103, 131, 107, 139, 181, 113, 151, 173, 167, 149, 197, 157, 211, 163, 223, 179, 229, 191, 257, 193, 239, 307, 199, 251, 277, 227, 283, 241, 233, 311