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@MISC{Leavens923x+1search,
    author = {Gary T. Leavens and Gary T. Leavens and Mike Vermeulen and Mike Vermeulen},
    title = {3x+1 Search Programs},
    year = {1992}
}

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Abstract:

Algorithms for computing peaks of certain statistics related to the 3x+1 problem are described, along with data on such peaks up to 56 trillion (5:6 2 10 13 ). The data result from several years of computation. The design of the algorithms used illustrates several techniques for program optimization. 1. Introduction The 3x + 1 problem concerns iterates of the following function: T (n) = ae (3n + 1)=2; if n j 1 (mod 2), n=2; if n j 0 (mod 2). (1) which takes odd integers n to (3n + 1)=2 and even integers n to n=2 [5]. The 3x + 1 Conjecture asserts that, starting from any positive integer n, repeated iteration of this function eventually produces the value 1. This conjecture is apparently intractable. The iterates of T are simply defined. Let T (0) (n) = n, and for all integers k ? 0, let T (k) (n) = T (T (k01) (n)). The sequence of iterates (T (0) (n); T (1) (n); T (2) (n); . . .) is called the T -trajectory of n. For example, the T -trajectory of 7 is: 7, 11, 17, 26...

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