On a Representation of the Collatz Procedure

NURİYEV U., Nuriyeva F.

6th International Conference on Problems of Cybernetics and Informatics, PCI 2025, Baku, Azerbaycan, 25 - 28 Ağustos 2025, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Doi Numarası: 10.1109/pci66488.2025.11219837
  • Basıldığı Şehir: Baku
  • Basıldığı Ülke: Azerbaycan
  • Anahtar Kelimeler: (:4+,-) Representation, Collatz Conjecture, Collatz Procedure, Computational Methods
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In this study, the Collatz Procedure is analyzed within the domain of odd numbers. These odd numbers are classified into two distinct subsets based on their modular characteristics. For each subset, a parameter is defined to reflect the transformation behavior under the Collatz operation. This classification enables a new symbolic representation of the procedure, which reveals the structural dynamics of number sequences more clearly. The paper investigates how the procedure operates within each subset and explores the transition rules that determine how a number moves between subsets during iteration.