On the 3x + 1 problem

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As to the conjecture that given m ε{lunate} N = {1,2,3,...}, the sequence {mn}n≥0, defined by the iterative formula m0 = m, mn+1 = mn 2, if mnis even, (3mn + 1) 2, if mnis odd, has some iterate mn = 1, it is shown in this note that for every real number ρ{variant} > 0, almost every m ε{lunate} N has some iterate mn < ρ{variant}m, or mj ≤ 2 for some j < n. Furthermore it is conjectured that ms(1 + s) ≤ 2 if s > 10 and m ≤ 2s. © 1989.




Venturini, G. (1989). On the 3x + 1 problem. Advances in Applied Mathematics, 10(3), 344–347. https://doi.org/10.1016/0196-8858(89)90018-3

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