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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 $n$?
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This problem is taken from the UKMT Mathematical Challenges.