More Jabber about the Collatz Conjecture and a Closed Form for Detecting   Cycles on Special Subsequences [Assertion: Collatz cycles]
  Professor Cadogan at the University of the West Indies identified special starting points that yield long subsequences where the normalization constant, k, is always one. I studied these special sequences and found an implicit mixed integer equation in closed form which if solved would produce seed values in cycling subsequences. Such cycles only occur among extremely large numbers, causing the equation to be difficult to solve numerically. 
Thomas W. Lynch
cs.DM