The rules are simple:
Take any number $n$. If $n$ is even divide it by two, if $n$ is odd triple it and subtract one. Repeat indefinitely. (Note that this is a variation, in the original Collatz conjecture you add one.)
Like the original Collatz conjecture seems to always get to one, this variation always seems to get to either $1, 7$ or $17$. I checked that it does for initial values of $n$ up to 443 million.
Can you give a number that doesn't get to $1$, $7$ or $17$, or if not, at least show that such number exists?