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.