Funny how now matter where they start out, just about everybody who attempts to take on the 3x+1 problem eventually ends up in pretty much the same place:
In 2007, researchers Kurtz and Simon, building on earlier work by J.H. Conway in the 1970s,[8] proved that a natural generalization of the Collatz problem is algorithmically undecidable.[7]
In 2007, researchers Kurtz and Simon, building on earlier work by J.H. Conway in the 1970s,[8] proved that a natural generalization of the Collatz problem is algorithmically undecidable.[7]
From http://en.wikipedia.org/wiki/Collatz_conjecture