The 3n+1 conjecture is about strictly *positive* integers - the (non-zero, just in case) natural numbers. One of the first things you do in research is search for what has been done.
There is plenty of writing out there about this conjecture, related conjectures, and undecidability. All written by experts, and my field does not overlap any of the areas involved. You're better off with them.
I'm not sure what more I can do other than say 'undecidability is not about randomness'. It is sort of like saying 'the colour green has nothing to do with the smell of bread'. I don't know that I have any simple examples.