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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the nonexistence of $2$-cycles for the $3x+1$ problem
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by John L. Simons PDF
Math. Comp. 74 (2005), 1565-1572 Request permission


This article generalizes a proof of Steiner for the nonexistence of $1$-cycles for the $3x+1$ problem to a proof for the nonexistence of $2$-cycles. A lower bound for the cycle length is derived by approximating the ratio between numbers in a cycle. An upper bound is found by applying a result of Laurent, Mignotte, and Nesterenko on linear forms in logarithms. Finally numerical calculation of convergents of $\log _2 3$ shows that $2$-cycles cannot exist.
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Additional Information
  • John L. Simons
  • Affiliation: University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
  • Email:
  • Received by editor(s): February 13, 2003
  • Received by editor(s) in revised form: May 4, 2004
  • Published electronically: December 8, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1565-1572
  • MSC (2000): Primary 11J86, 11K60; Secondary 11K31
  • DOI:
  • MathSciNet review: 2137019