Collatz Conjecture $$ a_{n} = \begin{cases} \frac{1}{2} a_{n-1} &\text{for} \quad a_{n-1} \quad \text{even} \\ 3 a_{n-1} +1 &\text{for} \quad a_{n-1} \quad \text{odd} \end{cases} $$ For more information see Wolfram MathWorld