### 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: On the density of happy numbers

Speaker: **Justin Gilmer**, Rutgers University

Date: Thursday, October 13, 2011 5:00pm

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

Abstract:

Consider the map which sends a positive integer to the sums of the squares of its digits. A number is defined to be happy if by iterating this map you eventually arrive at 1. Richard Guy inspired the study of happy numbers in his book Unsolved Problems in Number Theory (2nd Ed.). The distribution of happy numbers appears to be quite chaotic and to date little is known about their density. In this talk we use some probabilistic methods combined with computer number crunching to show that the upper and lower densities are at least 18% and at most 12% respectively.

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