If all the conjectures made in this paper are intractable, where would one
begin to do research on this deceptively simple problem?
As a guide to doing research, I ask questions.
Here are a few that occur to me:
For the 3x+1 problem, what restrictions are there on the growth in size
of members of a divergent trajectory assuming that one exists?
What interesting properties does the function have?
Is there some direct characterization of
other than the recursive definition (2.33)?