3x + 1 problem Articles The Recursive Stopping Time Structure of the 3x + 1 function (2017), latest update linkNew Results on the Stopping Time Behavior of the Collatz 3x + 1 Function (2015)On the Structure and the Behavior of Collatz 3n + 1 Sequences (2014) Directed Collatz graphs Special tree structure up to 341Special tree structure up to column 6