Number Theory


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

Authors: W.B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

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.

Comments: 10 Pages.

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[v1] 2016-11-07 11:29:42

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