Modified Collatz conjecture or (3a + 1) + (3b + 1)I Conjecture for Neutrosophic Numbers 〈Z ∪ I〉

Authors

  • W.B. Vasantha Kandasamy
  • K. Ilanthenral
  • Florentin Smarandache

Keywords:

Collatz Conjecture, Modified Collatz Conjecture, Neutrosophic Numbers

Abstract

Abstract: In this paper, a modified form of Collatz conjecture for neutrosophic numbers áZ È Iñ is defined. We see for any n Î áZ È Iñ the related sequence using the formula (3a + 1) + (3b + 1)I converges to any one of the 55 elements mentioned in this paper. Using the akin formula of Collatz conjecture viz. (3a- 1) + (3b -1)I the neutrosophic numbers converges to any one of the 55 elements mentioned with appropriate modifications. Thus, it is conjectured that every n Î áZ È Iñ has a finite sequence which converges to any one of the 55 elements.

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Published

2016-12-15

Issue

Vol. 14 (2016): Neutrosophic Sets and Systems

Section

SI#1,2024: Neutrosophical Advancements And Their Impact on Research

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

 Creative Commons Attribution (CC BY) license.

How to Cite

Kandasamy, W. V. ., K. Ilanthenral, & Florentin Smarandache. (2016). Modified Collatz conjecture or (3a + 1) + (3b + 1)I Conjecture for Neutrosophic Numbers 〈Z ∪ I〉 . Neutrosophic Sets and Systems, 14, 44-46. http://fs.unm.edu/nss8/index.php/111/article/view/572