Proposing a Novel Collatz Representation of Numbers to Establish a Different Approach in proving the Collatz Conjecture

Aditya Dalal

doi:https://doi.org/10.14445/22315373/IJMTT-V67I11P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 11 | Year 2021 | Article Id. IJMTT-V67I11P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I11P506

Proposing a Novel Collatz Representation of Numbers to Establish a Different Approach in proving the Collatz Conjecture

Aditya Dalal

Abstract

This paper proposes a novel representation of natural numbers in order to provide a framework for solving the Collatz Conjecture. The paper also through a series of direct and inductive proofs shows how these number representations called the Collatz Representation can be used to find the number of steps for a number to reach 1 according to the Collatz Conjecture while also identifying patterns.

Keywords

Collatz Conjecture, Hailstone Sequence, Induction.

References

[1] Bart S., Matt T., The Collatz Problem and Analogues, Journal of Integer Sequences, 11 (2008).

Citation :

Aditya Dalal, "Proposing a Novel Collatz Representation of Numbers to Establish a Different Approach in proving the Collatz Conjecture," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 11, pp. 47-53, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I11P506