The 3n p Conjecture: A Generalization of Collatz Conjecture
*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
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.
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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, 2017Copy 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, 2017Available from: https://www.ultrascientist.org/paper/774/
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