Corpus ID: 14437934

The 3x+1 Problem: An Annotated Bibliography, II (2000-2009)

@article{Lagarias2006The3P,
  title={The 3x+1 Problem: An Annotated Bibliography, II (2000-2009)},
  author={J. Lagarias},
  journal={arXiv: Number Theory},
  year={2006}
}
  • J. Lagarias
  • Published 2006
  • Mathematics
  • arXiv: Number Theory
  • The 3x+1 problem concerns iteration of the map T(n) =(3n+1)/2 if n odd; n/2 if n even. The 3x +1 Conjecture asserts that for every positive integer n>1 the forward orbit of n includes the integer 1. This paper is an annotated bibliography of work done on the 3x+1 problem published from 2000 through 2009, plus some later papers that were preprints by 2009. This is a sequel to an annotated bibliography on the 3x+1 problem covering 1963-1999. At present the 3x+1 Conjecture remains unsolved. 
    44 Citations

    Paper Mentions

    The real 3x + 1 problem
    • 5
    • PDF
    Generalized Collatz Functions: Cycle Lengths and Statistics
    • 2
    • PDF
    Clusters of Integers with Equal Total Stopping Times in the 3x + 1 Problem
    The 3n + 1 Problem: A Probabilistic Approach
    Convergence of generalized Collatz problem in k-adic field
    An algebraic fractal approach to Collatz Conjecture
    On Collatz Conjecture
    Order in the Collatz: Fractal Symmetry Controlling Syracuse Function Trajectories

    References

    SHOWING 1-10 OF 109 REFERENCES
    A new statistic for the 3x + 1 problem
    • 10
    • PDF
    THE 3x +1 PROBLEM AND DIRECTED GRAPHS
    • 14
    • PDF
    The 3x + 1 semigroup
    • 10
    • Highly Influential
    • PDF
    Structure Theorem for (d, g, h)-Maps
    • 15
    • Highly Influential
    • PDF
    The generalized 3x + 1 mapping
    • 9
    ON TOTAL STOPPING TIMES UNDER 3x + 1 ITERATION
    • 8
    • PDF
    The sufficiency of arithmetic progressions for the 3+1 Conjecture
    • 10
    • PDF
    The proof of the hypothesis about “3x+1”
    • 1
    The real 3x + 1 problem
    • 5
    • PDF