Bounds for the 3x+1 problem using difference inequalities

@article{Krasikov2003BoundsFT,
  title={Bounds for the 3x+1 problem using difference inequalities},
  author={I. Krasikov and J. Lagarias},
  journal={Acta Arithmetica},
  year={2003},
  volume={109},
  pages={237-258}
}
  • I. Krasikov, J. Lagarias
  • Published 2003
  • Mathematics
  • Acta Arithmetica
  • We study difference inequality systems for the 3x+1 problem introduced by the first author in 1989. These systemes can be used to give lower bounds for the number of integers below x that contain 1 in their forward orbit under the 3x+1 map. Previous methods gave away some information in these inequalities. We give an improvement which apparantly extracts full information from the inequalities. By computer aided proof we show that at least x^{0.84} of the integers below x contain 1 in their… CONTINUE READING
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