Collatz conjecture revisited: an elementary generalization

Collatz conjecture states that iterating the map that takes even natural number n to n2{n \over 2} and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting results are obtained. Since Collatz conjecture can be seen as a particular case of the generalization introduced in this articule, several more general conjectures are also presented.