@inbook{
author = "Fabiano, Nicola and Mirkov, Nikola S. and Mitrović, Zoran D. and Radenović, Stojan",
year = "2023",
abstract = "We discuss and give some insights on the Collatz conjecture, known as 3N + 1, and Kurepa’s hypothesis on the left factorial. First, the Collatz conjecture is considered and the density of values is compared to Planck’s black body radiation in physics, showing a remarkable agreement between the two. We also briefly discuss a generalization of Collatz conjecture for a generic sequence qN +1 by means of numerical analysis. Then, we give a brief historical excursus and prove in a simple way some properties of Kurepa’s function, also called the left factorial. We introduce Kurepa’s hypothesis, propose a new description, and the relation to Bezout’s parameters and the Diophantine equation. A numerical analysis supports Kurepa’s hypothesis and the conjecture about distribution for Kurepa’s function.",
journal = "Advances in Number Theory and Applied Analysis",
booktitle = "Collatz Hypothesis and Kurepa’s Conjecture",
pages = "31-50",
doi = "10.1142/9789811272608_0003"
}