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幸运数

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幸运数是经由类似埃拉托斯特尼筛法的算法后留下的整数集合,是在1955年波兰数学家乌拉姆提出。

由一组由1开始的数列为例:

1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,...

先将所有偶数删去,只留下奇数

1,    3,    5,    7,    9,   11,   13,   15,   17,   19,   21,   23,   25,...

然后把数列中的第个数字(设该数字为)的倍数对应的数删除,即把所有第个数删除,例如上述例子中,第数字是,所以删去所有第个数:

1,    3,          7,    9,         13,   15,         19,   21,         25,...

新数列的第项(每次都加上)为,因此将新数列的第个数删除:

1,    3,          7,    9,         13,   15,               21,         25,...

若一直重复上述的步骤,最后剩下的数就是幸运数OEISA000959:

137913152125313337434951636769737579879399......
示明筛选幸运数过程的动画,其中红色的数字为幸运数。

幸运数有部分特性和素数相同,例如幸运数的分布情形也可用素数定理来分析,而哥德巴赫猜想孪生素数猜想也有以幸运数为基准的版本。

幸运数有无限多个。但目前不确定是否存在无限个幸运素数(lucky prime):

3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, ...
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幸运数
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