A Clustering Perspective of the Collatz Conjecture

José A. Tenreiro Machado, Alexandra Galhano and Daniel Cao Labora
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José A. Tenreiro Machado: Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
Alexandra Galhano: Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
Daniel Cao Labora: Department of Statistics, Mathematical Analysis and Optimization, Faculty of Mathematics, Institute of Mathematics (IMAT), Universidade de Santiago de Compostela (USC), Rúa Lope Gómez de Marzoa s/n, 15782 Santiago de Compostela, Spain

Mathematics, 2021, vol. 9, issue 4, 1-14

Abstract: This manuscript focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The first part of the paper is devoted to describe the problem, providing a historical introduction to it, as well as giving some intuitive arguments of why is it hard from the mathematical point of view. The second part is dedicated to the visualization of behaviors of the Collatz iteration function and the analysis of the results.

Keywords: multidimensional scaling; Collatz conjecture; clustering methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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