2021/05/05 by Tobías Canavesi, Tobias Canavesi, Canavesi, Tobias
Computer Science · Mathematics · #Benford’s Law and Fraud Detection #Collatz conjecture #Combinatorics #Conjecture #Digital Media Forensic Detection #Discrete mathematics #FOS: Mathematics #Fibonacci number #General Mathematics (math.GM) #Graph #Mathematics #Number theory #Sequence (biology) #math.GM
paper · pdf · doi:10.48550/arxiv.2105.04415
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/05/05 · openalex publication_date 2021/05/05 · arxiv updated 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Considering all possible paths that a natural number can take following the rules of the algorithm proposed in the Collatz conjecture we construct a graph that can be interpreted as an infinite network that contemplates all possible paths within the conjecture. This allows us to understand why the minimal element of the Collatz orbit x is equal to 1. Subsequently we define the extended Collatz conjecture equal to o x+1 when x is odd and x/2 when x is even with o an odd number greater than 3 and we show that there are infinite orbits in the extended Collatz conjecture that diverges. Finally, we find interesting theorems relating the Fibonacci sequence to prime numbers.