The 3n + 1 Problem Spring 2014
A JavaScript implementation
The Conjecture: For any positive integer $ n $, the iterates
$ f^{1}(n) = f(n), f^{2}(n) = f(f(n)), f^{3}(n) = f(f^{2}(n)), \dots, f^{k}(n), \dots $
of the function
$$ f(n) = \left\{
\begin{array}{ll}
\frac{n}{2} & {\text{ if }} n {\text{ is even}} \\
3n + 1 & {\text{ if }} n {\text{ is odd}}
\end{array}
\right.
$$
will eventually produce the value 1; that is, $f^{m}(n) = 1$ for some positive integer $m$.
Prof. A. O. Hausknecht, Mathematics, UMass Dartmouth