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Professor Cadogan at the University of the West Indies identified specialstarting points that yield long subsequences where the normalization constant,k, is always one. I studied these special sequences and found an implicit mixedinteger equation in closed form which if solved would produce seed values incycling subsequences. Such cycles only occur among extremely large numbers,causing the equation to be difficult to solve numerically.

More Jabber about the Collatz Conjecture and a Closed Form for Detecting Cycles on Special Subsequences [Assertion: Collatz cycles]