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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 $t_{2008}$?




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This problem is taken from the UKMT Mathematical Challenges.