Collatz 3x+1 Conjecture

An iteration on the integers (n, not x, is used for integers here):

    T_s(n)= 3*n+1 when n in {1[2]}
     T_s(n)=n/2 when n in {0[2]}

Conjecture: Any positive integer n produces a trajectory which converges to 1.

E.g.   13 => 40 => 20 => 10 => 5 => 16 => 8 => 4 => 2 => 1
(1 => 4 => 2 => 1,  provides a terminating infinite loop.)

This can be pictured as general predecessor tree.    (I show and consider only the odd integers.)