Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method-Reference-Cited by-同舟云学术

Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method

Published:2022-06-08 Issue:12 Volume:10 Page:1972
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Orús-Lacort Mercedes^ORCID,Jouis Christophe

Abstract

In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in analyzing the sequence generated by odd numbers, we can deduce a formula for the general term of the Collatz sequence for any odd natural number n after several iterations. This formula is used in one case that we analyze using the mathematical complete induction method in the process of demonstrating the conjecture.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/10/12/1972/pdf

Reference18 articles.

1. Lothar Collatz;O’Connor,2006

2. Logo: A Retrospective;Maddux,1997

3. Wonders of Numbers;Pickover,2001

4. Gödel, Escher, Bach;Hofstadter,1979

5. E17: Permutation Sequences;Guy,2004

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Stochastic-like characteristics of arithmetic dynamical systems: the Collatz hailstone sequences;Journal of Physics: Complexity;2024-02-19

2. Applied Computing and Artificial Intelligence;Mathematics;2023-05-15

3. An Asymptotic Approach for the Collatz Conjecture;Information;2023-03-15

4. Analysis of the Romanian Capital Market Using the Fractal Dimension;Fractal and Fractional;2022-10-04