Stage: 5 Challenge Level:
The sequence can start anywhere and it is only practical to test a
few starting values. The problem is to prove results that show that
all the number chains reduce to a few that can be listed.
This problem is a simple example of a dynamical system,
demonstrating fixed points and cyclic or periodic behaviour. It is
instructive to work with such 'whole number dynamics' as an
introduction to dynamical systems leading to useful applications as
the Logistic Equation for population dynamics and to fractals and
the well known Mandelbrot set.