To understand the "hailstone sequence", try reversing the process. All 3n+1 can be divided by 2 once, twice, or more. When the process is reversed, those which take three or more divisions serve as the basis of ever increasing "hailstone sequence" lengths terminating at the various demonstrable "odd entry gates".
To understand the "hailstone sequence", try reversing the process. All 3n+1 can be divided by 2 once, twice, or more. When the process is reversed, those which take three or more divisions serve as the basis of ever increasing "hailstone sequence" lengths terminating at the various demonstrable "odd entry gates".