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[数论] Flavius Josephus筛子

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hbghlyj Posted 2023-1-3 22:22 |Read mode
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19...每2项删除一项
1   3   5   7   9    11    13    15    17    19...每3项删除一项
1   3       7   9          13    15          19...每4项删除一项
1   3       7              13    15          19...每5项删除一项
.... 永远继续下去,剩下的是序列$a_n$(OEIS), 证明$a_n$不是5的倍数.

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选定 60 周期(易检验周期性), 作六次操作即可归纳得结论. 具体哪些质数倍数被剔除有空再想.  Posted 2023-1-3 23:26

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Czhang271828 Posted 2023-1-3 23:30
以及, 推测是 OEIS 上寻找 $2023$ 时发现的?

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默认sort: relevance的首条结果🙂  Posted 2023-1-4 05:24

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 Author| hbghlyj Posted 2023-1-4 05:35
Czhang271828 发表于 2023-1-3 16:26
具体哪些质数倍数被剔除有空再想.
猜测只有2和5🙂

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en.wikipedia.org/wiki/Josephus_problem
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