Collatz 3n+1 Problem Structure I've finished putting up all the content I can think of concerning a structure I've developed about the Collatz 3n+1 problem. Mathematicians who refer to the problem as the 3x+1 problem were never brainwashed by FORTRAN (as I was) into the belief that n, not x, stands for an integer. I hope someone who can formalize mathematical proofs will see the potential here ...

Collatz Problem ...

Computational verification of the 3x+1 conjecture Introduction Results References Links Contact Introduction Let x be an integer. Let the function T(x) be equal to (3x+1)/2 if x is odd and equal to x/2 if x is even. The 3x+1 conjecture , asserts that starting from any positive integer n the repeated iteration of T(x) eventually produces the integer 1, after which the iterates will alternate ...

A paper by Peter Schorer describing a new approach to the 3x + 1 Problem, an approach based on two remarkably simple structures that underlie the 3x + 1 function. The paper includes a possible solution to the Problem.

International Conference on the Collatz Problem and Related Topics August 5-6, 1999 Katholische Universitat Eichstatt, GERMANY This conference is intended for anyone interested in the 3x+1 problem ( also known as the Syracuse algorithm, Collatz', Kakutani's, or Ulam's problem), and related mathematics. CONFIRMED INVITED SPEAKER: Jeffrey C. Lagarias, AT&T Labs The LOCATION of the conference, ...

An Image From the Collatz Problem By Andrew Shapira February 15, 1998 (Minor revisions such as web link updates were made subsequently.) Introduction Consider the following rule that maps a given positive integer n to another: if n is even, the next integer is n/2; if n is odd, the next integer is 3n+1. Starting at an arbitrary integer, we can repeatedly apply the rule to obtain a sequence of ...