The 3x+1 problem: new lower bounds on nontrivial cycle lengths

@article{Eliahou1993The3P,
  title={The 3x+1 problem: new lower bounds on nontrivial cycle lengths},
  author={Shalom Eliahou},
  journal={Discrete Mathematics},
  year={1993},
  volume={118},
  pages={45-56}
}
Eliahou, S., The 3x+ 1 problem: new lower bounds on nontrivial cycle lengths, Discrete Mathematics 118 (1993) 45556. Let 7’: N -+ N be the function defined by T(n) = n/2 if n is even, T(n) = (3n + 1)/2 if n is odd. We show, among other things, that any nontrivial cyclic orbit under iteration of T must contain at least 17 087 915 elements. 

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