Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Brian Nakamura, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu
Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Mining for Primes in the Field of Continued Fractions and Linearly Recursive Sequences

Speaker: Arthur DuPre, Rutgers University

Date: Thursday, September 20, 2012 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ


We show how to generate sequences of primes from the process of multiplying continued fractions of a certain form by positive integers. One of these sequences, A000057, has been in OEIS, for over forty years, placed there by Neil Sloane himself. Some of the sequences of primes we generate can also be more quickly generated via linearly recursive sequences, and for some, we have not yet found a corresponding recurrent sequence, although we conjecture there is one. We will also describe potentially fruitful procedures to generate more prime sequences not yet discovered.

See: http://www.math.rutgers.edu/~bnaka/expmath/