A(n)个数码,恰好分成k个数,k个数积最大

王守恩

前面的有问题吗？来个反例就行。谢谢！

天马行空往前走一走！

256——16——基本解。
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

256——16——"0"是可以去掉的。
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1,

256——16——相同数码的"行"是可以去掉的。
8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9,
7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7,
6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5,
4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3,
2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1,

256——16——相同数码的"列"也是可以去掉的。
8, 8, 8, 9, 9, 9, 9,
7, 7, 8, 7, 7, 7, 7,
7, 7, 7, 6, 6, 7, 7,
6, 6, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 4, 5,  
4, 4, 4, 3, 4, 3, 3,
2, 3, 2, 2, 2, 2, 2,  
2, 2, 2, 2, 2, 2, 1,
1, 1, 1,  

256——16——每个数 - 1。
7, 7, 7, 8, 8, 8, 8,
6, 6, 7, 6, 6, 6, 6,
6, 6, 6, 5, 5, 6, 6,
5, 5, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 3, 4,  
3, 3, 3, 2, 3, 2, 2,
1, 2, 1, 1, 1, 1, 1,  
1, 1, 1, 1, 1, 1, 0,
0, 0, 0,  
256——16——去掉"0"。
7, 7, 7, 8, 8, 8, 8,
6, 6, 7, 6, 6, 6, 6,
6, 6, 6, 5, 5, 6, 6,
5, 5, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 3, 4,  
3, 3, 3, 2, 3, 2, 2,
1, 2, 1, 1, 1, 1, 1,  
1, 1, 1, 1, 1, 1,

256——16——每个数 - 1。
6, 6, 6, 7, 7, 7, 7,
5, 5, 6, 5, 5, 5, 5,
5, 5, 5, 4, 4, 5, 5,
4, 4, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 2, 3,  
2, 2, 2, 1, 2, 1, 1,
0, 1, 0, 0, 0, 0, 0,  
0, 0, 0, 0, 0, 0,

256——16——去掉末尾"0"——结论没变。
6, 6, 6, 7, 7, 7, 7,
5, 5, 6, 5, 5, 5, 5,
5, 5, 5, 4, 4, 5, 5,
4, 4, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 2, 3,  
2, 2, 2, 1, 2, 1, 1,
0, 1,   

王守恩

hujunhua 发表于 2025-8-6 09:48
2ab=(a+b)^2-(a-b)^2
所以分成子集拼成两个数时，保持和最大，差最小，则乘积最大。
和最大，要求大数字占 ...

A = {1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,......},

R(1)=1,——A(1)个数码, 恰好分成1个1位数, 当1个数的积最大时,  最小1位数=R(1)。
R(2)=32, ——A(4)个数码, 恰好分成2个2位数, 当2个数的积最大时,  最小2位数=R(2)。
R(3)=763, ——A(9)个数码, 恰好分成3个3位数, 当3个数的积最大时,  最小3位数=R(3)。
R(4)=6642, ——A(16)个数码, 恰好分成4个4位数, 当4个数的积最大时,  最小4位数=R(4)。
R(5)=77531, ——A(25)个数码, 恰好分成5个5位数, 当5个数的积最大时,  最小5位数=R(5)。
R(6)=875421, ——A(36)个数码, 恰好分成6个6位数, 当6个数的积最大时,  最小6位数=R(6)。
R(7)=8865421,
R(8)=88754321,
R(9)=887654321,
R(10)=9876543210,
R(11)=98765543210,
R(12)=987765433210,
R(13)=9877665433210,
R(14)=98876554432210,
R(15)=988766554332110,
R(16)=9887766544322110,
R(17)=98887665544322110,
R(18)=988877655443322110,
R(19)=
R(20)=

尊敬的 hujunhua！您是我的引路人(很多帖子我还在经常回看)。OEIS没有这串数,麻烦您去申报(这串数是您的)。谢谢！