a(n) = the smallest positive integer such that neither a(n) nor a(n)+1 are coprime to A024619(n), where A024619 is the sequence of positive integers that are not powers of primes.

22 is the 9th positive integer that is not a power of a prime. a(9) = 10 because neither 10 nor 10+1=11 is coprime to 22, and 10 and 11 are the smallest pair of consecutive positive integers where this is the case.