A057467 GCD of n-th and (n+1)-st term in the sequence of first differences between primes, A001223.

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 6, 2, 2, 2, 2, 2, 2, 12, 4, 2, 2, 2, 2, 2, 2, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 4, 4, 4, 4, 2, 6, 2, 2, 6, 2, 2, 6, 2, 2