@article{ApplegateLagarias2006,
  author    = {{David Applegate and Jeffrey C. Lagarias}},
  title     = {{The $3x+1$ semigroup}},
  journal   = {{J. Number Theory}},
  year      = {{2006}},
  volume    = {{177}},
  pages     = {{146--159}},
  note      = {{MR 2006k:11037}},
}