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Age 14 to 16 Short Challenge Level:

The first term of a sequence of positive integers is $6$. The other terms in the sequence follow these rules:

                if a term is even then divide it by $2$ to obtain the next term;
                if a term is odd then multiply it by $5$ and subtract $1$ to obtain the next term.

For which values of $n$ is the $n$th term equal to $n$?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.