The Conjecture asserts that all trajectories of positive n are
convergent.
It is certainly true for n > 1 that
cannot occur without some occurring.
Call the least
positive k for which the
stopping time of n, and set if no k occurs
with .
Also call the least positive k for which
the total stopping time of n, and set
if no such k occurs.
We may restate the Conjecture in terms of the stopping time
as follows.