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<math>^n{a} =
<math>^n{a} =
\begin{cases}
\begin{cases}
1, & \mbox{if }n\mbox{=0} \\
1, & \mbox{if }n\mbox{ =0} \\
a^{[(n-1)a]}, & \mbox{if }n\mbox{ >0}
a^{a^^{(n-1)}}, & \mbox{if }n\mbox{ >0}
\end{cases}</math>
\end{cases}</math>
\begin{cases}
n/2, & \mbox{if }n\mbox{ is even} \\
3n+1, & \mbox{if }n\mbox{ is odd}
\end{cases}
==Examples==
==Examples==