I spent a considerable amount of time starting in 1981, helped by collaborators Tony Watts, George Leigh and Bob Buttsworth, studying certain aspects of the 3x+1 problem (Collatz problem) and related problems. The starting point was a paper of Herbert Möller (Über Hasses Verallgemeinerung des Syracuse-Algorithmus (Kakutanis Problem), Acta Arith. 34 (1978) 219-226) which related the 3x+1 problem to 2-adic analysis.
The 3x+1 problem is a special case of a more general class of problems which are equally tantalizing, but about which one can make accurate predictions.
