A047947 Schinzel's rhobar(n), number of distinct lengths of a block of consecutive integers on which a maximum of n primes occurs infinitely often (under the k-tuple conjecture).

2, 4, 2, 4, 4, 4, 6, 4, 2, 4, 6, 6, 2, 6, 4, 6, 4, 6, 4, 4, 6, 4, 6, 10, 4, 6, 6, 4, 6, 4, 6, 6, 4, 2, 4, 6, 8, 6, 4, 2, 8, 4, 10, 2, 4, 10, 10, 4, 6, 6, 2, 10, 6, 2, 6, 4, 6, 12, 4, 6, 10, 4, 6, 6, 6, 8, 6, 10, 4, 8, 6, 6, 2, 6, 12, 10, 2, 4, 6, 6, 8, 4, 2, 10, 8, 6, 6, 4, 8, 10, 2, 6, 4, 2