4 papers
The sequence of Collatz functions, exceptionality of the 3n+1 function and the notion of Collatz generalized Matrix
Raouf Rajab
In this article, we define a very important sequence of functions, all the functions of this sequence present behaviors very close to that of the Collatz function. The study of suc…
Classification of Collatz infinite sequences
Raouf Rajab
In the present paper, we are interested in classifying of Collatz sequences on based to the different behavior of these sequences when their lengths tend to infinity. A Collatz inf…
General formulas of global characteristic coefficients of Collatz function
Raouf Rajab
The purpose of this paper is to show three general formulas of three global characteristic coefficients of Collatz function. The Collatz function is defined by the following operat…
The fundamental properties characterizing the structural behaviors of Collatz sequences
Raouf Rajab
This work represents an in-depth study of the structural behavior of the Collatz sequences. We consider a finite arithmetic progression with a common difference is 2 and the number…