The 3n+1 Collatz Problem

This problem has a mysterious history and it is not easy to explain the attraction of mathematicians for it. Consider f(n)=n/2 in n is even and f(n)=(3n+1)/2 if n is odd. It is true that, for all n, the orbit of n by f ends in the cycle (1-2)? The answer for this question is unknown and a lot of problems have borned in the research of this answer (e.g. it is true that the conjecture holds for a set A of positive density? (answer: unknown). Or, if the orbit of n by f is bounded it ends in the cycle (1-2)? (answer: unknown)). We study several aspects of the dynamical system defined by function f and several generalizations of this function.

Members Active in this Field (at IME-USP)

  1. Manuel Valentim de Pera Garcia - (e-mail mane@ime.usp.br)
  2. Fabio Armando Tal - (email fabiotal@ime.usp.br )

Publications

  1. A note on the generalized 3n+1 problem - Manuel V. P. Garcia and Fabio A. Tal - Acta Arithmetica XC 3 (1999) pp. 245-250
mane at ime.usp.br
Up to research fields in applied math