The 3n  p Conjecture: A Generalization of Collatz Conjecture

Author:
W.B. VASANTHA KANDASAMY*, ILANTHENRAL KANDASAMY** and FLORENTIN SMARANDACHE**
Affiliation:

*Department of Mathematics, IIT Madras, Chennai, India

**School of Computer Science and Engineering, VIT University, Vellore, India

***Department of Mathematics, University of New Mexico, USA

Corresponding Author E-mail : vasanthakandasamy@gmail.com

Keyword:
Collatz Conjecture; Kakutani’s Conjecture ; 3n 1 Conjecture; 3n  p Conjecture
Issue Date:
February, 2017
Abstract:

The Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutanis problem (after Shizuo Kakutani) and so on. Several various generalization of the Collatz conjecture has been carried. In this paper a new generalization of the Collatz conjecture called as the 3n  p conjecture; where p is a prime is proposed. It functions on 3n  p and 3n  p , and for any starting number n , its sequence eventually enters a finite cycle and there are finitely many such cycles. The 3n 1 conjecture, is a special case of the 3n  p conjecture when p is 1.

Pages:
83-88
ISSN:
2319-8044 (Online) - 2231-346X (Print)
Source:
DOI:
http://dx.doi.org/10.22147/jusps-A/290207
Share This:
Facebook Twitter Google Plus LinkedIn Reddit

Copy the following to cite this article:

W.B. VASANTHA KANDASAMY*, ILANTHENRAL KANDASAMY** and FLORENTIN SMARANDACHE**, "The 3n  p Conjecture: A Generalization of Collatz Conjecture", Journal of Ultra Scientist of Physical Sciences, Volume 29, Issue 2, Page Number 83-88, 2017

Copy the following to cite this URL:

W.B. VASANTHA KANDASAMY*, ILANTHENRAL KANDASAMY** and FLORENTIN SMARANDACHE**, "The 3n  p Conjecture: A Generalization of Collatz Conjecture", Journal of Ultra Scientist of Physical Sciences, Volume 29, Issue 2, Page Number 83-88, 2017

Available from: https://www.ultrascientist.org/paper/774/the-3n-p-conjecture-a-generalization-of-collatz-conjecture

Ansari Education And Research Society
Facebook Google Plus Twitter