The 3x +1 Conjecture is simple to state and apparently intractably hard to solve. ... Despite this doleful pronouncement, study of the 3x +1 problem has not been without reward. ...

"The 3x + 1 problem and its generalizations". American Mathematical Monthly 92 (1 ): 3?23. ... Keith Matthews' 3x +1 page: Review of progress, plus various programs ...

Density Bounds for the 3x +1 Problem I. Tree-Search Method , ... Density Bounds for the 3x +1 Problem II. Krasikov Inequalities . David Applegate and ...

Despite this doleful pronouncement, study of the 3x +1 problem has not been without reward. ... A Continuous Extension of the 3x +1 Problem to the Real Line , Dynamics of ...

open 3X + 1 problem , but it is an implicit consequence of some recent work ... rational coe?cients (generalization of the 3x + 1 problem ) Studies in ...

The 3x +1 problem is one I find interesting as it is based on some ... The 3x +1 equation appears to connect all the positive integers into a tree rooted on the ...

... a new approach to the 3x + 1 Problem , an approach based on two remarkably simple structures that underlie the 3x + 1 function. ...

The 3x +1 Problem is perhaps today's most enigmatic unsolved mathematical ... The problem is also referred to as the 3n + 1 problem and is associated with ...

x/2, and maps all odd numbers x to (3x + 1 )/2, the s-orbit of any positive integer. contains 1 . This problem is simple to state and therefore seems easy to tackle. ...

The 3x +1 conjecture [1 ], [2, problem E16] asserts that starting from any positive integer ... In order to test the 3x +1 conjecture, in 1996 we wrote a computer program (in the ...