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Stage: 4 Short Challenge Level: Challenge Level:1

The terms of the sequence are

$$6, 3, 14, 7, 34, 17, 84, 42, 21, 104, 52, 26, 13, 64, 32, 16, 8, 4, 2, 1, 4, 2, 1, \dots$$

As can be seen, there will now be no other terms in the sequence other than $4$, $2$, and $1$. It can also be seen that the only values of $n$ for which the $n$th term equals $n$ are $13$ and $16$.

This problem is taken from the UKMT Mathematical Challenges.