Is a Solution to the 3 x + 1 Problem in Sight? The 3x + 1 Problem (also known as the Syracuse Problem) asks if repeated iterations o f the basic formula (3x + 1)/(2 ~d'(3~+1)) always terminate in 1, where x is an odd positive integer, and ord2(y) is the largest power o f 2 that divides y. Thus, e.g., beginning with x = 3, one iteration yields 5, the next iteration yields 1. The Problem is traditionally attributed to Lothar Collatz, who discovered it during his student days in the 1930s. It is still unsolved, although more than 150 papers on :it have been published. The best summaries o f results that I am aware of are (Lakarias 1985) and (Lakarias I996). One reason the Problem has proved so difficult is that there does not seem to be any pattern to the computations produced by iterations of the basic formula. For example, the successive odd iterates for x = 7 are 11, 17, 13, 5, 1. For x = 15 they are 23, 35, 53, 5, 1. Forx = 21, there is only one iterate, namely, 1. But for 27 there are 41 iterates: 41, 31,
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Is a solution to the 3 x + 1 problem in sight?
Schorer, Peter
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, Volume 28 (4)
Association for Computing Machinery – Dec 1, 1997
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