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评论
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0.从自然数序列开始:
s0=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,。。。
1.删除每10个术语:
s1=1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21,22,。。。
2.删除每10个术语:
s2=1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,21,23,24,。。。
执行10次后,我们有:
s10=1,2,3,4,5,6,7,8,9,21,23,25,27,29,32,35,38,42,46,49,。。。
此算法可以推广到
“删除每个第k个术语k次!”。我们有
k=2:s2=1,5,9,13,17,21,25,29,33,37,41,45,。。。a(n)=4n-3(n=1,2,…)
k=3:s3=1,2,7,10,14,16,20,23,28,29,34,37,41,43,47,50,55,(这里没有简单的规则,还有其他规则?)
k=4:s4=1,2,3,9,11,14,18,22,23,29,30,33,38,39,43,46,50,51
k=5,s5=1,2,3,4,11,13,16,19,23,26,28,32,34,39,41,42,48,51,52
k=6,s6=1,2,3,4,5,13,15,17,20,23,27,31,32,37,38,44,45,47,52,53
k=7,s7=1,2,3,4,5,6,15,17,19,22,25,29,33,34,38,39,44,45,51,52,54
k=8,s8=1,2,3,4,5,6,7,17,19,21,23,26,29,33,37,39,42,44,47,50,53
k=9,s9=1,2,3,4,5,6,7,8,19,21,23,25,28,31,34,38,42,43,47,48,52,
a_k(n)有什么一般规则吗?
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