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For n > 2, a(n) is the smallest novel number whose least non divisor prime is the greatest prime divisor of a(n-1). Let p be the smallest prime which does not divide a(n-1). If rad(a(n-1)) = A002110(k), p = prime(k+1), otherwise p is the smallest prime < Gpf(a(n-1) which does not divide a(n-1).

The terms of the sequence can be extracted from the table in A125703, where the k-th row gives numbers whose least non divisor prime p is the k-th prime. From a(5) onwards the first appearance of q = Gpf(a(n-1)) = prime(k) gives a(n) = A002110(k-1), the first term in the k-th row of A125703. Subsequent appearances of same q selects a(n) from the same row. The primes q = Gpf(a(n-1)) decrement from term to term if rad(a(n-1) is in A002110, and occasionally we see a full cycle of q from some higher prime terminating at q = 2 (see Example). However this is rare, because of interruptions when rad(a(n-1)) is not primorial, causing q to increment before decrementing again. This retards the arrival of odd numbers in the sequence. Whereas we may suppose that all numbers in A125703 will eventually appear, the blocking of full decremetation cycles of q produces a "firewall" effect opposing this possibility. Conjecture: Full cycles of decrementing q conclude with a(n) a power of 2 (producing the next odd term).