A075610 a(1) = 1, a(n) = smallest prime number not occurring earlier such that the concatenation a(n-1) and a(n) is a composite number.

1, 2, 5, 7, 11, 13, 3, 19, 17, 29, 23, 31, 41, 37, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 97, 89, 103, 101, 109, 107, 113, 127, 131, 137, 139, 149, 151, 167, 157, 173, 163, 179, 181, 191, 193, 197, 199, 223, 227, 211, 233, 229, 239, 241, 251, 269, 263, 271, 257, 277