ON A CLASS OF SOLVABLE RECURRENCES WITH PRIMES
We investigate an interesting new class of “greatest prime factor sequences” in which every term is the greatest prime factor of the sum of all of the preceding terms. We show that these sequences are explicitly solvable, satisfying a fairly regular growth pattern. Thus, if is the nth prime, then the number of occurrences of each large enough is By using a known upper bound for the gaps between consecutive primes, it turns out that the asymptotic estimate holds true.
greatest prime factor, recurrent sequences, prime gaps.