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

Abstract

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.

42 pages; will be periodically updated, cover papers till 2009+ later papers preprints by 2009; sequel to arxiv:math.NT/0309224; v4 now runs from 2000 rather than 2001, 121 entries; v5 40 pages, 126 entries, v6 42 pages, 134 enries

References in corpus (4)

• Benford's Law, Values of L-functions and the 3x+1 Problem
• Affine actions of a free semigroup on the real line
• The 2-adic valuation of a sequence arising from a rational integral
• Some Observations on the 3x+1 Problem

Cited by in corpus (18)

• The 3x+1 Problem and Integer Representations
• The 3x+1 Problem: An Overview
• A window to the Convergence of a Collatz Sequence
• Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps
• Two different scenarios when the Collatz Conjecture fails
• On the Foundations of the Theory of a new Collatz Based Number System
• A matricial view of the Collatz conjecture
• On Collatz Conjecture
• Integer patterns in Collatz sequences
• The intricate labyrinth of Collatz sequences
• Some considerations on Collatz conjecture
• Consecutive Integers and the Collatz Conjecture
• Clusters of Integers with Equal Total Stopping Times in the 3x + 1 Problem
• lrsarith: a small fixed/hybrid arithmetic C library
• The Collatz Problem generalized to 3x+k
• Encoding and Visualization in the Collatz Conjecture
• $7x\pm 1$: Close Relative of Collatz Problem
• Collatz Problem of Positive Integers