Optimal bounds for the length of rational Collatz cycles

• Autorzy: Lorenz Halbeisen , Norbert Hungerbühler
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996-1997
• Tom: 78
• Numer: 3
• Strony: 227-239

Daty

wydano

1997

otrzymano

1995-09-14

poprawiono

1995-11-16

Twórcy

autor

Lorenz Halbeisen

• Mathematik Departement, ETH Zürich, CH-8092 Zürich, Switzerland

autor

Norbert Hungerbühler

• IMA, University of Minnesota, 514 Vincent Hall, 206 Church Street S.E., Minneapolis, Minnesota 55455, U.S.A.

Bibliografia

• [1] R. E. Crandall, On the 3x+1 problem, Math. Comp. 32 (1978), 1281-1292.
• [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.
• [3] S. Eliahou, The 3x+1 problem: New lower bounds on nontrivial cycle lengths, Discrete Math. 118 (1993), 45-56.
• [4] I. Krasikov, How many numbers satisfy the 3x+1 conjecture ? Internat. J. Math. Sci. 12(4) (1989), 791-796.
• [5] J. C. Lagarias, The 3x+1-problem and its generalizations, Amer. Math. Monthly 92 (1985), 3-23.
• [6] J. C. Lagarias, The set of rational cycles for the 3x+1 problem, Acta Arith. 56 (1990), 33-53.
• [7] G. Leavens and M. Vermeulen, private communication.
• [8] J. W. Sander, On the (3N+1)-conjecture, Acta Arith. 55 (1990), 241-248.
• [9] B. G. Seifert, On the arithmetic of cycles for the Collatz-Hasse(Syracuse) conjectures, Discrete Math. 68 (1988), 293-298.
• [10] G. Wirsching, An improved estimate concerning 3n+1 predecessor sets, Acta Arith. 63 (1993), 205-210.