求{1, 2, ..., 100}没有等和对的最大子集

王守恩

A345731——1, 2, 4, 7, 12, 18, 24, 34, 45, 57, 71, 86, 105, 126, 150, 171,

a(1)=0,  0,
a(2)=1,  0, 1,
a(3)=2,  0, 1, 2,
a(4)=4,  0, 1, 2, 4,
a(5)=7,  0, 1, 2, 4, 7,
a(6)=12,  0, 1, 2, 4, 7, 12,
a(7)=18,  0, 1, 2, 4, 8, 13, 18,
a(8)=24,  0, 1, 2, 4, 8, 14, 19, 24,
a(9)=34,  0, 1, 2, 4, 8, 15, 24, 29, 34,
a(10)=45,  0, 1, 7, 10, 13, 21, 26, 41, 43, 45,
a(11)=57,
a(12)=71,
a(13)=86,
a(14)=105,
a(15)=126,
a(16)=150,
a(17)=171,

a(11)——a(17)鼓捣了几天也没鼓捣出来, 只能怪——A345731——这也太小气了——后面不是有大把地皮吗？！
# A345731 (b-file synthesized from sequence entry)
2 1
3 2
4 4
5 7
6 12
7 18
8 24
9 34
10 45
11 57
12 71
13 86
14 105
15 126
16 150
17 171

王守恩

A345731——1, 2, 4, 7, 12, 18, 24, 34, 45, 57, 71, 86, 105, 126, 150, 171,

a(1)=0,  0,
a(2)=1,  0, 1,
a(3)=2,  0, 1, 2,
a(4)=4,  0, 2, 3, 4,
a(5)=7,  0, 3, 5, 6, 7,
a(6)=12,  0, 1, 2, 6, 9, 12,
a(7)=18,  0, 1, 2, 4, 8, 13, 18,
a(8)=24,  0, 1, 2, 4, 8, 14, 19, 24,
a(9)=34,  0, 1, 2, 4, 8, 15, 24, 29, 34,
a(10)=45,  0, 1, 7, 10, 13, 21, 26, 41, 43, 45,

a(11)=57,——鼓捣不出来——这是个错家伙——各位！可有答案？谢谢！！

Table[Solve[{a1 ≠ a2 ≠ a3 ≠ a4 ≠ a5 ≠ a6 ≠ a7 ≠ a8 ≠ a9 ≠ n ≠ a1 + a2 ≠ a1 + a3 ≠ a2 + a3 ≠ a1 + a4 ≠ a2 + a4 ≠ a3 + a4 ≠ a1 + a5 ≠ a2 + a5 ≠ a3 + a5 ≠ a4 + a5
≠ a1 + a6 ≠ a2 + a6 ≠ a3 + a6 ≠ a4 + a6 ≠ a5 + a6 ≠ a1 + a7 ≠ a2 + a7 ≠ a3 + a7 ≠ a4 + a7 ≠ a5 + a7 ≠ a6 + a7 ≠ a1 + a8 ≠ a2 + a8 ≠ a3 + a8 ≠ a4 + a8 ≠ a5 + a8 ≠ a6 + a8 ≠ a7 + a8
≠ a1 + a9 ≠ a2 + a9 ≠ a3 + a9 ≠ a4 + a9 ≠ a5 + a9 ≠ a6 + a9 ≠ a7 + a9 ≠ a8 + a9 ≠ a1 + n ≠ a2 + n ≠ a3 + n ≠ a4 + n ≠ a5 + n ≠ a6 + n ≠ a7 + n ≠ a8 + n ≠ a9 + n,
a1 < a2 < a3 < a4 < a5 < a6 < a7 < a8 < a9 < n}, {a5, a6, a7},  PositiveIntegers], {a1, 1, 1}, {a2, 2, 2}, {a3, 4, 12}, {a4, a3 + 6, 20}, {a8, 51, 51}, {a9, 54, 54}, {n, 57, 57}]
无端感觉(前面的都是这样):  a8, a9, n = 等差数列。

王守恩

A345731——1, 2, 4, 7, 12, 18, 24, 34, 45, 57, 71, 86, 105, 126, 150, 171,

a(1)=0,  0,
a(2)=1,  0, 1,
a(3)=2,  0, 1, 2,
a(4)=4,  0, 2, 3, 4,
a(5)=7,  0, 3, 5, 6, 7,
a(6)=12,  0, 1, 2, 6, 9, 12,
a(7)=18,  0, 1, 2, 4, 8, 13, 18,
a(8)=24,  0, 1, 2, 4, 8, 14, 19, 24,
a(9)=34,  0, 1, 2, 4, 8, 15, 24, 29, 34,
a(10)=45,  0, 1, 7, 10, 13, 21, 26, 41, 43, 45,

a(11)=57,——这是个错家伙——各位！可有答案？谢谢！！

王守恩

前面的都能出来。就这个"57"出不来！谢谢！！！

1. While[True, set=Join[{0}, Sort[RandomSample[Range[1, 57], 10]]]; sums=Total /[url=home.php?mod=space&uid=6175]@[/url] Subsets[set, {2}]; If[Length[sums]==Length[Union[sums]], Break[]];]; set

复制代码

northwolves

王守恩 发表于 2025-7-17 08:16
A345731——1, 2, 4, 7, 12, 18, 24, 34, 45, 57, 71, 86, 105, 126, 150, 171,

a(1)=0,  0,

a(5)=7： {{0, 1, 2, 4, 7}, {0, 3, 5, 6, 7}}
a(6)=12：{{0, 1, 2, 4, 7, 12}, {0, 1, 2, 6, 9, 12}, {0, 3, 6, 10, 11, 12}, {0, 5, 8, 10, 11, 12}}
a(7)=18：{{0,1,2,4,8,13,18},{0,1,2,7,10,14,18},{0,4,8,11,16,17,18},{0,5,10,14,16,17,18}}
a(8)=24：{{0,1,2,4,8,14,19,24},{0,5,10,16,20,22,23,24}}
a(9)=34：{{0,1,2,4,8,15,24,29,34},{0,1,2,7,13,16,26,30,34},{0,1,2,14,19,24,27,30,34},{0,4,7,10,15,20,32,33,34},{0,4,8,18,21,27,32,33,34},{0,5,10,19,26,30,32,33,34}}

王守恩

通过这几天的磨练,手工解题思路很清晰。

譬如,{0,5,10,16,20,22,23,24}}

10+5=15,——从第3个数开始看。
16+5=21,16+10=26——看后面的数{20,22,23,24}, 会不会有{21,26}。
20+5=25,20+10=30,20+16=36,——看后面的数{22,23,24}, 会不会有{25,30,36}。
22+5=27,22+10=32,22+16=38,22+20=42,——看后面的数{23,24}, 会不会有{27,32,38,42}。
23+5=28,23+10=33,23+16=39,23+20=43,23+22=45,——看后面的数{24}, 会不会有{28,33,39.43,45}。
24,——最后1个数,不用看。

northwolves

59可行：   {{0, 1, 2, 4, 8, 15, 28, 37, 49, 54, 59}, {0, 1, 2, 4, 13, 25, 32, 39, 49, 54, 59}}
58也可行：   {0, 1, 2, 22, 29, 39, 43, 47, 52, 55, 58}

northwolves

Largest cliques in connected supermagic graphs

mathe

Best depth: 11
1 2 6 10 18 32 34 45 52 55 58
Best depth: 12
1 2 3 8 13 23 38 41 55 64 68 72

mathe

Best depth: 13
1 2 12 18 22 35 43 58 61 73 80 85 87