Abstract
We investigate an interesting new class of "greatest prime factor sequences" {u n} n≥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 nth 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.
Original language | English (US) |
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Pages (from-to) | 197-208 |
Number of pages | 12 |
Journal | JP Journal of Algebra, Number Theory and Applications |
Volume | 26 |
Issue number | 2 |
State | Published - Sep 1 2012 |
Externally published | Yes |
Keywords
- Greatest prime factor
- Prime gaps
- Recurrent sequences
ASJC Scopus subject areas
- Algebra and Number Theory