Maximum excursion and stopping time record-holders for the problem: Computational results
Maximum excursion and stopping time record-holders for the problem: Computational results
复制标题
该问题的最大偏移和停止时间记录保持者：计算结果
DOI：
10.1090/s0025-5718-99-01031-5
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
T. E. O. Silva
中科院分区：
文献类型：
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作者：
T. E. O. Silva
本文提出了一些有关搜索所谓3x+1问题的初始值的结果比所有较小的初始值的值。我们的计算结果表明，对于n的初始值，函数迭代的最大值从上面的n 2 f（n）界定，而f（n）的常数或非常缓慢地增加n的函数。作为此（详尽）搜索的副产品，该搜索的执行最多为n。 =3。253 2.702。 10 16，3x + 1的猜想被验证到相同的数字。
This paper presents some results concerning the search for initial values to the so-called 3x+1 problem which give rise either to function iterates that attain a maximum value higher than all function iterates for all smaller initial values, or which have a stopping time higher than those of all smaller initial values. Our computational results suggest that for an initial value of n, the maximum value of the function iterates is bounded from above by n 2 f(n), with f(n) either a constant or a very slowly increasing function of n. As a byproduct of this (exhaustive) search, which was performed up to n. = 3. 2 53 2.702. 10 16 , the 3x + 1 conjecture was verified up to that same number.