58. The behavior of some very simple dynamical systems is still not completely known. Consider the system that starts with a positive whole number and gives as the next number

This iterative function system was devised by Lothar O. Collatz, later of the University of Hamburg, during his student days before World War II. It is sometimes called the “ problem” or the “Syracuse problem” (because it became popular in the Mathematics Department of Syracuse University), and the sequences generated are sometimes referred to as hailstone numbers.

What you observe is known to happen for all , but after more than 60 years, mathematicians have been unable to show that it happens for every whatsoever.