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