3 papers
math.GM2026
Paradoxical behavior in Collatz sequences
Olivier Rozier, Claude Terracol
On the set of positive integers, we consider the iterative process that maps to either or depending on the parity of . The Collatz conjecture…
math.NT2025
Are the Collatz and abc conjectures related?
Olivier Rozier
The Collatz and conjectures, both well known and thoroughly studied, appear to be largely unrelated at first sight. We show that assuming the conjecture true is helpful…
math.DS2025
Parity sequences of the 3x+1 map on the 2-adic integers and Euclidean embedding
Olivier Rozier
In this paper, we consider the one-to-one correspondence between a 2-adic integer and its parity sequence under iteration of the so-called "3x+1" map. First, we prove a new formula…