Optimal bounds for the length of rational Collatz cycles

Lorenz Halbeisen; Norbert Hungerbühler

Acta Arithmetica (1997)

  • Volume: 78, Issue: 3, page 227-239
  • ISSN: 0065-1036

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Lorenz Halbeisen, and Norbert Hungerbühler. "Optimal bounds for the length of rational Collatz cycles." Acta Arithmetica 78.3 (1997): 227-239. <http://eudml.org/doc/206944>.

@article{LorenzHalbeisen1997,
author = {Lorenz Halbeisen, Norbert Hungerbühler},
journal = {Acta Arithmetica},
keywords = {Collatz problem; problem; rational Collatz cycles; iteration; length},
language = {eng},
number = {3},
pages = {227-239},
title = {Optimal bounds for the length of rational Collatz cycles},
url = {http://eudml.org/doc/206944},
volume = {78},
year = {1997},
}

TY - JOUR
AU - Lorenz Halbeisen
AU - Norbert Hungerbühler
TI - Optimal bounds for the length of rational Collatz cycles
JO - Acta Arithmetica
PY - 1997
VL - 78
IS - 3
SP - 227
EP - 239
LA - eng
KW - Collatz problem; problem; rational Collatz cycles; iteration; length
UR - http://eudml.org/doc/206944
ER -

References

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  1. [1] R. E. Crandall, On the 3x+1 problem, Math. Comp. 32 (1978), 1281-1292. Zbl0395.10013
  2. [2] J. M. Dolan, A. F. Gilman and S. Manickam, A generalization of Everett's result on the Collatz 3x+1 problem, Adv. in Appl. Math. 8 (1987), 405-409. Zbl0648.10009
  3. [3] S. Eliahou, The 3x+1 problem: New lower bounds on nontrivial cycle lengths, Discrete Math. 118 (1993), 45-56. Zbl0786.11012
  4. [4] I. Krasikov, How many numbers satisfy the 3x+1 conjecture ? Internat. J. Math. Sci. 12(4) (1989), 791-796. Zbl0685.10008
  5. [5] J. C. Lagarias, The 3x+1-problem and its generalizations, Amer. Math. Monthly 92 (1985), 3-23. Zbl0566.10007
  6. [6] J. C. Lagarias, The set of rational cycles for the 3x+1 problem, Acta Arith. 56 (1990), 33-53. Zbl0773.11017
  7. [7] G. Leavens and M. Vermeulen, private communication. 
  8. [8] J. W. Sander, On the (3N+1)-conjecture, Acta Arith. 55 (1990), 241-248. Zbl0707.11017
  9. [9] B. G. Seifert, On the arithmetic of cycles for the Collatz-Hasse(Syracuse) conjectures, Discrete Math. 68 (1988), 293-298. Zbl0638.10003
  10. [10] G. Wirsching, An improved estimate concerning 3n+1 predecessor sets, Acta Arith. 63 (1993), 205-210. Zbl0804.11022

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