Collatz-ish

A sequence is generated using these rules. For which values of n is the nth term equal to n?
Age
14 to 16
Challenge level
filled star filled star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



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.