2-adic parity explorations of the 3n+1 problem.

Francis Laclé (1)

1 Department of Information and Computing Sciences [Utrecht]

Starting with a separate 2-adic reformulation of the Collatz function that maps parity orbits, we show that the stopping time $k$ of this reformulation can be alternatively derived with the help of some novel ideas as well as hybrid-algorithmic techniques.

Mots clés: Adic spaces; Collatz Conjecture; Syracuse conjecture; Arc diagrams; Number theory

Domaines: Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]; Théorie des nombres [math.NT]; Anneaux et algèbres [math.RA]; Théorie des groupes [math.GR]; Combinatoire [math.CO]; Logiciel mathématique [cs.MS]; Analyse numérique [cs.NA]; Arithmétique des ordinateurs; Algèbre commutative [math.AC]; Systèmes dynamiques [math.DS]; Mathématiques générales [math.GM]

Francis Laclé. 2-adic parity explorations of the 3n+1 problem.. 2021. ⟨hal-03201180v2⟩