The 3x+1 problem: An annotated bibliography (1963--1999) (sorted by author)

Abstract

The 3x+ 1 problem concerns iteration of the map on the integers given by T(n) = (3n+1)/2 if n is odd; T(n) = n/2 if n is even. The 3x+1 Conjecture asserts that for every positive integer n > 1 the forward orbit of n under iteration by T includes the integer 1. This paper is an annotated bibliography of work done on the 3x+1 problem and related problems from 1963 through 1999. At present the 3x+1 Conjecture remains unsolved.

74 pages latex; 197 references, second title change to distinguish from 3x+1 book; first title change indicates abridgment of earlier versions to papers 1999 and earlier ; part II now covers papers 2000 and later, see arxiv:math.NT/0608208; v.11 cutoff date changed from 2000 to 1999, v.13 added Oulipo references

References in corpus (1)

• Benford's Law, Values of L-functions and the 3x+1 Problem

Cited by in corpus (10)

• The 3x+1 Problem and Integer Representations
• Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps
• On the Foundations of the Theory of a new Collatz Based Number System
• A matricial view of the Collatz conjecture
• Integer patterns in Collatz sequences
• $7x\pm 1$: Close Relative of Collatz Problem
• lrsarith: a small fixed/hybrid arithmetic C library
• The Collatz Problem generalized to 3x+k
• On the Collatz general problem $qn+1$
• Collatz Problem of Positive Integers