### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**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

Abstract:

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/