Weak and strong admissible triplets associated to Collatz like map

Abderrahman Bouhamidi (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

In this paper, we will study a class of Collatz like problems associated to what we will call weak or strong admissible triplets. This representation can be seen as a simple extension of the classical Collatz mapping, which will give rise to a tool for generating remarkable triplets with convergence to cycles by avoiding the obstacle of difficult Diophantine equations. Many special and interesting families of admissible triplets will be given as well as some general properties. We will establish some formulas for the corresponding map and for the total stopping time. Interesting conjectures which give rise to a general formulation to the classical Collatz conjecture will be given. Bound lengths for eventual non-trivial cycles will be studied and analyzed. Two algorithms will be given for determining automatically the lower bound length for an eventual cycle. Experimental results and test examples will be presented.

Keywords: Collatz conjecture; Number theory, Discrete mathematics, Collatz conjecture

Domains: Mathematics [math]

Abderrahman Bouhamidi. Weak and strong admissible triplets associated to Collatz like map. 2024. ⟨hal-04552296⟩