Published in Volume XIII, 2003, pages 1-16

Authors: Jeffrey R. GOODWIN


This paper presents a new way of approaching the Collatz Conjecture (3x+1 problem). Earlier work has shown the conjecture holds for sequences of odd integers of the form xi=4xi-1+1,i∈ N, i≥2 if the first term is known to terminate at 1. The new approach involves a technique for avoiding the need to calculate whether the first term terminates at 1. As a result, several sets of integers are described for which the conjecture holds. The subsequent patterns to the identities produced reveal the possibility of a new way of attempting a proof of the conjecture.


  title={Results on the Collatz Conjecture.},
  author={Jeffrey R. GOODWIN},
  journal={Scientific Annals of Computer Science},
  organization={``A.I. Cuza'' University, Iasi, Romania},
  publisher={``A.I. Cuza'' University Press}