<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Collatz conjecture states that iterating the map that takes even natural number n to
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2020-0007_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mi>n</mi><mn>2</mn></mfrac></mrow></math><tex-math>{n \over 2}</tex-math></alternatives></inline-formula>
and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting results are obtained. Since Collatz conjecture can be seen as a particular case of the generalization introduced in this articule, several more general conjectures are also presented.</p></abstract>

Collatz conjecture states that iterating the map that takes even natural number n to
n2{n \over 2}
and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting results are obtained. Since Collatz conjecture can be seen as a particular case of the generalization introduced in this articule, several more general conjectures are also presented.

Collatz conjecture revisited: an elementary generalization

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Collatz conjecture revisited: an elementary generalization"}

Collatz conjecture states that iterating the map that takes even natural number n to
n2{n \over 2}
and odd natural number n to 3n + 1, will eventually obtain...

Collatz conjecture revisited: an elementary generalization

Publié en ligne: 16 juil. 2020

Pages: 112 - 127

Reçu: 16 août 2019

DOI: https://doi.org/10.2478/ausm-2020-0007

Mots clés
Collatz conjecture

© 2020 Amauri Gutierrez, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Collatz conjecture revisited: an elementary generalization

Publié en ligne: 16 juil. 2020

Pages: 112 - 127

Reçu: 16 août 2019

DOI: https://doi.org/10.2478/ausm-2020-0007

Mots clésCollatz conjecture

© 2020 Amauri Gutierrez, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Collatz conjecture