By Wilson's theorem, p! == 1 (mod p+2) whenever (p,p+2) are twin primes. This sequence and A286181 concern consecutive primes (p,q) satisfying p! = 1 (mod q), where d = q-p > 2.
It follows that (d-1)! == 1 (mod q). Listed terms correspond to d = 12, 30, 76 (cf. A286230). Further terms should have d>=140.
Also, primes q=prime(n) such that A275111(n-1)=1, and (prime(n-1),prime(n)) are not twin primes (i.e., q is not a term of A006512).