# On a Class of Solvable Recurrences with Primes (journal paper)

Year:

2012
Researcher(s):

Mihai Caragiu, Alexandru Zaharescu (UIUC), and Mohammad Zaki
Institution:

Ohio Northern University
Discipline:

Mathematics **Abstract**: We investigate an interesting new class of “greatest prime factor sequences” (u_n)_{n\ge 1} 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 p_n is the *n-*th prime, then the number of occurrences of each large enough p_n is p_{n+1}-p_{n-1} By using a known upper bound for the gaps between consecutive primes, it turns out that the asymptotic estimate u_n=(n/2)+O(n^0.525) holds true.

Publication Information:

JP Journal of Algebra, Number Theory and Applications Volume 26, Issue 2, Pages 197 - 208 (September 2012)