problem are most elegantly expressed in
terms of iterations of the function
One way to think of the 
problem involves a directed graph whose
vertices are the positive integers and that has directed edges from n
to 
.
I call this graph the Collatz graph of 
in honor of
L. Collatz [25].
A portion of the Collatz graph of 
is pictured in Fig. 1.
A directed graph is said to be weakly connected
if it is connected when viewed as an undirected graph,
i.e., for any two vertices there is a path of edges joining them,
ignoring the directions on the edges.
The 
Conjecture can be formulated in terms of the
Collatz graph as follows.
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