Weekly Problem 46 - 2012
A sequence of positive integers $t_{1},t_{2}, t_{3}, t_{4}, ...$ is defined by:
$t_{1}=13$
$t_{n+1}=\frac{1}{2}t_{n}$ if $t_{n}$ is even
$t_{n+1}=3t_{n}+1$ if $t_{n}$ is odd.
What is the value of $t_{2008}$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.