4 papers · 1 filter
Characteristic numbers and characteristic equations of parity vectors of Collatz sequences
Raouf Rajab
The present work deals with the characterization of parity vectors of Collatz sequences (of finite and infinite length). Such a characterization leads to the determination of sever…
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…
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…