TITLE: What is the simplest collatz like problem that is undecidable?
QUESTION [6 upvotes]: I have read that problems resemblings collatz have been shown to be undecidable.
Conway proved that apparantly but Im not sure if the proof was constructive.
So I wonder : What is the simplest collatz like problem that is undecidable ?

REPLY [5 votes]: I don't know about simplest, but this answer by Gerry Myerson cites two papers that prove that some natural generalizations of the Collatz problem are undecidable:

Conway, "Unpredictable iterations", 1972
Kurtz and Simon, "The Undecidability of the Generalized Collatz Problem", 2007

There is also a more recent, quite short paper:

Lehtonen, Two undecidable variants of Collatz’s problems, 2008
the PDF seems freely available