xilihutu
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加入时间: 2007/03/29
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来自: 美国
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作者：xilihutu 在 驴鸣镇 发贴, 来自 http://www.hjclub.org
Basic properties
The sequence grows indefinitely. In fact, any variant defined by starting with a different seed number will (eventually) also grow indefinitely, except for the degenerate sequence 22, 22, 22, 22 ... .
No digits other than 1, 2, and 3 ever appear in the sequence, unless the seed number contains such a digit or a run of more than three of the same digit.
Conway's cosmological theorem: Every sequence eventually splits into a sequence of "atomic elements", which are finite subsequences that never again interact with their neighbors. There are 92 elements containing the digits 1,2,3 only, which John Conway named after the natural chemical elements. There are also two "transuranic" elements for each digit larger than 3.
The terms eventually grow in length by about 30% per generation. In fact, if Ln denotes the number of digits of the n-th member of the sequence, then
where is an algebraic number of degree 71 known as Conway's constant. This fact was proven by Conway. This also holds for variants of the sequence starting with any integer other than 22.
Conway's constant is the unique positive real root of the following polynomial:
作者：xilihutu 在 驴鸣镇 发贴, 来自 http://www.hjclub.org |
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再考才子：有一数列。。。
