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