a(n) is the least prime from the union {2,3} and A164333, beginning with which the n-th prime p_n is obtained by some number of iterations of the S operator g(see A164960).

The sequence is connected with our sieve selecting the primes of the union {2,3} and A164333 from all primes. Note that a(n)=n iff p_n is in the considered union, which corresponds to 0's iterations of g.