悬赏挑战：求2025的两两之差乘积最大的堆磊数组

mathe

对于\(x_0=0,x_1=1,x_2=2,...,x_h=h,x_{h+1}\gt h+1,x_{h+2},\cdots, x_n\)
前\(h+1\)个数两两之间差的乘积为\(h!(h-1)!\cdots1!\), 而两个数之间至少有一个数不在前h+1个的，我们根据它们下标的差距进行分类，下标差距为1的乘积有
\(\D(x_{h+1}-x_h)(x_{h+2}-x_{h+1}\cdots(x_n-x_{n-1})\le (\frac{x_n-h}{n-h})^{n-h}\)
下标差距为2的乘积有
\(\D(x_{h+1}-x_{h-1})(x_{h+2}-x_h)\cdots(x_n-x_{n-2})\le (\frac{x_n+x_{n-1}-2h+1}{n-h})^{n-h}\)
...
下标差距为h+1的乘积有
\(\D(x_{h+1}-x_0)(x_{h+2}-x_1)\cdots(x_n-x_{n-h-1})\le (\frac{x_n+\cdots+x_{n-h}-\frac{h(h+1)}2}{n-h})^{n-h}\)
下标差距为h+2的乘积有
\(\D(x_{h+2}-x_0)(x_{h+3}-x_1)\cdots(x_n-x_{n-h-2})\le (\frac{x_n+\cdots+x_{n-h-1}-\frac{(h+1)(h+2)}2}{n-h-1})^{n-h-1}\)
...
下标差距为n-1的只有两项
\(\D(x_{n-1}-x_0)(x_n-x_1) \le (\frac{x_n+x_{n-1}-1}2)^2\)
下标差距为n的只有一项
\(x_n-x_0=x_n\)
在假设n个数之和为给定数S的情况下，我们知道
\(\D x_n+x_{n-1}+...+x_{t+1}\le S-(1+2+...+t)=S-\frac{t(t+1)}2\)
由此得出乘积不超过
\(\D(\prod_{i=1}^hi!) (\prod_{d=1}^{h+1}(\frac{S-\frac{(n-d)(n-d+1)}2-\frac{(2h-d+1)d}2}{n-h})^{n-h})(\prod_{d=1}^{n-h-1}(\frac{S-\frac{(n-d)(n-d+1)}2-\frac{d(d-1)}2}d)^d)\)
所以如果搜索过程退到一定的h, 如果发现对所有可用的n,这些上界都小于已知最优结果，就不需要继续搜索了。

mathe

对于上一楼中，我们考虑h=0的情况，也就是对所有\(x_1,x_2,\cdots,x_n\)不做任何限制的场景下n+1个数时
那么可以得到乘积上界在n为奇数时是
\(U_n=\frac{(S-\D\frac{n^2-1}4)^{\frac{n+1}2}\D\prod_{h=0}^{\frac{n-3}2}(S-h(h+1))^{n+1}}{\prod_{h=1}^n h^h}\)
而乘积上界在n为偶数时是
\(U_n=\frac{\D\prod_{h=0}^{\frac{n-2}2}(S-h(h+1))^{n+1}}{\D\prod_{h=1}^n h^h}\)
特别的，在S是三角数时，这个上界对于最大的n显然是正好能够取到的。
我们比较\(U_n,U_{n+1}\)可以发现对于稍微大一点的S,由于\(S\ge \frac{n(n+1)}2, h\lt n/2\),得出\(U_n\)应该是严格递增的，由此我们证明如果S正好是三角数, 必然能够取到最大n对应的\(U_n\),也就是这时必然序列为\(x_h=h\).
比如对于偶数n, \(\D\frac{U_n}{U_{n-1}}=\frac{(S-\frac{n^2-2n}4)^{\frac n2+1}\D\prod_{h=0}^{\frac{n-4}2}(S-h(h+1))}{n^n}\), 分子约为\((\frac n2)^{2n}\)大于分母，所以递增。 n为奇数时类似。

而对于S不是三角数时，用类似方案，通过提供一个最大n时的特解，如果能够证明这个结果大于\(U_{n-1}\)就可以证明对于较大的S,总是需要使用最大n值,于是在此约束下，就很容易得出前面必须一批连续的数字

有了上面这个结论，对于S=2025就比较容易了，由于1+2+...+63=2016, 我们只需要穷举将9变成不减序列的和的形式，累加到1,2,...,63末尾即可。
当然现在还余下很多细节，比如这个方案多于多大的S才开始成立

mathe

上面还是算错了，应该是
\(U_{S,n}=\frac{\prod_{h=1}^n (S-\frac{(n-h+1)(n-h)}2 - \frac{h(h-1)}2)^{n-h+1}}{\prod_{h=1}^nh^h}\)
直接比较\(U_{S,n}\)和\(U_{S,n-1}\)还是有些困难。但是应该适合计算机计算，可以将太小的n给淘汰。
比如S=100, 我们可以计算\(U_{S,n}\)如下:
n U
1 100.00000000000000000000000000000000000
2 242574.75000000000000000000000000000000
3 7872548284.4814814814814814814814814815
4 2164371030540288.0000000000000000000000
5 3305388914821917619852.5000000000000000
6 18177369188840769514982208219.418608829
7 222960640592907929479532195595000675.04
8 3.4822080670484952383429062821087128968 E42
9 3.4692052259441463007579054093671361964 E49
10 8.9596486527759842405342579031680910006 E55
11 1.7108357477975209610095963225102936782 E61
12 3.5370828263899711924754514008153482141 E64
13 2.5138327076945574607196507368934914668 E64
在使用长度13搜索到最优解
100:        {0,1,2,3,4,5,6,7,8,9,10,12,15,18}:        11921006725876381088060832067876080433932691046400000000000000 ~=1.19E61
后，根据上面估计式，就可以避免搜索n<11的部分，继续搜索完n=12和n=11。

wayne

我给出Mathematica的代码。100的结果是

1. {13,{1,2,3,4,5,6,7,8,9,10,12,15,18}}

复制代码

1. Block[{s = 100, n, exp}, n = Floor[1/2 (-1 + Sqrt[1 + 8 s])];
   
2. product = 0; ans = {};
   
3. Do[params =Array[a, i];
   
4.   exp = Total[params] == s && Less @@ Flatten[{0, params, s}];
   
5.   Do[ppro = Times @@ Abs[Subsets[p, {2}] . {1, -1}];
   
6.    If[ppro > product, product = ppro; ans = {i, p}], {p, SolveValues[exp, params, Integers]}], {i, n}]; ans]

复制代码

王守恩

2——2——2——0,
5——3——3——1,
9——4——4——2,
14——23——5——2,
20——24——6——3,
27——33——6——4,
35——223——7——4,
44——224——8——5,
54——233——8——6,
65——234——9——7,
77——2223——9——7,
90——2224——10——8,
104——2233——10——9,
119——2234——11——10,
135——21234——12——10,
152——22223——11——11,
170——22224——12——12,
189——22233——12——13,
209——22234——13——14,  
230——212234——14——14,  
252——212324——14——15,   
275——212333——14——16,
299——222224——14——17,
324——222233——14——18,
350——222234——15——19,  
377——2122234——16——19,
405——2122324——16——20,
434——2122333——16——21,  
464——2122334——17——22,
495——2222224——16——23,  
527——2222233——16——24,  
560——2222234——17——25,
594——21222234——18——25,  
629——8位数
665——8位数,
702——8位数
740——8位数
779——8位数
819——8位数
860——8位数
902——9位数
第4排表示:譬如299——17,299是使用0-17连续数的最后一个。324——18,324是使用0-18连续数的最后一个。377——19,377是使用0-19连续数的最后一个。
第4排有规律——0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 14, 14, 15,..., 特别地可以把2, 4, 7, 10, 14, 19, 25, 32, 40, 49, 59, ...提出来。
第3排=第2排的和——没有规律。
第2排: 只能用1234四个数码。第1位=2，1在第2位(最多用1次)，4在最后位((最多用1次))，3只能在2的后面。4位数有4个；5位数有5个；6位数有6个；7位数有7个；
第1排(这是最复杂的一串数)。上下2个数之间的数：基本上是按照从第1个数重新开始。可又不完全是这样！
应该没有通项公式！丢了！！！！！！
要不，多组解的来几个。譬如：{{9,3,  {6,2,1},  240},    {9,3,  {5,3,1},  240}}.看能不能来点灵感。谢谢！

mathe

我们看看能否找到比较适合计算机计算的更好裁剪方案，以S=100为例子，我们可以先搜索n=13找到这个范围最优结果约1.19E61,
然后上面统一分析只排除了n<11, 对于n=12,我们可以考虑下面的一个看起来应该不错基准排列方案:
{0,1,2,3,4,5,6,7,8,9,10,11,12} + {1,2,3,4,5,7}={0,1,2,3,4,5,6,8,10,12,14,16,19}
也就是将0+1+...+12用完后还余下22继续使用1+2+3+4+5+6,发现还余下1，再将1加到最后。
然后我们查看不等式
$x_1/1*x_2/2*x_3/3*x_4/4*x_5/5*x_6/6*x_7/8*x_8/10*x_9/12*x_10/14*x_11/16*x_12/19*(x_2-x_1)/1*(x_3-x_1)/2*(x_4-x_1)/3*(x_5-x_1)/4*(x_6-x_1)/5*(x_7-x_1)/7*(x_8-x_1)/9*(x_9-x_1)/11*(x_10-x_1)/13*(x_11-x_1)/15*(x_12-x_1)/18*(x_3-x_2)/1*(x_4-x_2)/2*...*(x_12-x_11)/3
\le (((1/1-1/1-1/2-1/3-1/4-1/5-1/7-1/9-1/11-1/13-1/15-1/18)x_1+(1/2+1/1-1/1-1/2-1/3-1/4-1/6-1/8-1/10-1/12-1/14-1/17)x_2+(1/3+1/2+1/1-1/1-1/2-1/3-1/5-1/7-1/9-1/11-1/13-1/16)x_3+...+(1/19+1/18+1/17+1/16+1/15+1/14+1/13+1/11+1/9+1/7+1/5+1/3)x_12)/78)^{78}$
然后不等式右边括号里面分子部分是一个一次表达式，而且结果必然是正数，我们可以改为在约束条件
$x_1\ge 1, x_2\ge x_1+1, x_3\ge x_2+1,...,x_12\ge x_11+1, x_1+x_2+...+x_12=100$的线性约束条件下求上面分子的最大值（不限定为整数），这样就可以得到一个上界估计。
而上面不等式右边分子各项系数化简后为
[-109751/60060, -16973/14280, -493189/720720, -5/24, 925/2772, 1921/1560, 676/1155, 159/280, 2681/3960, 315449/360360, 60545/48048, 102641317/77597520]
可以看出最后一项系数最大,那么这种情况肯定是最后一个值越大结果越大，所以我们在右边选择\(x_1=1,x_2=2,...,x_{11}=11,x_{12}=12+22\)代入，可以得到右边结果上界约422.649。由此得到n=12时乘积的一个上界为422.649*muldiff{0,1,2,3,4,5,6,8,10,12,14,16,19}=7.948E59, 小于n=13的最优值1.19E61说明n=12不需要搜索。类似应该可以判断n=11

mathe

应用前面的思路，可以给出一个改进的代码，现在寻找S=2025的整数解已经非常容易了
scl.zip (37.56 KB, 下载次数: 2)

3 天前 上传

点击文件名下载附件

附件中代码会遍历最大n的情况，然后对较小n计算U(S,n),如果发现U(S,n)大于已经最大n场景，在利用上面新方法来验证对应的n是否还有可能产生较优的解。
然后对各S进行计算，计算结果在scl3.out中，可以看出，对于部分S还是不能完全判断成功，理论上对于这些情况我们只需要在搜索次大的n然后继续验证即可，不过这部分代码我还没有添加上。
而对于S=2025,得到最优结果为
2025:n=63        {4,3,1,1}:        1815078288564672078542467843546253122879141228711536847006602962292138806146805599904689148711562245766917612181881281791493989946064780650817524112456617650320182464723005866314986545404763704462250181767096814252182925029092772719423071858657048564193002505381832761656854377692302533439886475240768135842072097007541840236898577893196420328652661988352490748449382595009479708225414100314448121914917360393389211115050179675039779093613446064741748061791467971697514057376672766752204704060505224580974596954388370358075573433478830884238574883395860374668858816482186557965183877052171920466448034378173892554921621192617600268126700650147163721239854120765132593754031353076832743176202765186778288522117495692344379372147967696896022904184165734843210647018484887442567436041398714054162964704137981019573574107366238757022700205161135826893621064735596299139913086460319119539206197365459219875590232801266343996998682053211871604416483530639919112648193735717105927540724623224167594057745972698015558485573385825402577398428759539233492029668278141505336303665170647478838034585791000421306714764251486407003839712191964385397827852254167069808231888726929550404637306915797829914343122649914673764749128692931592721140245520698094108350918148846496494130391050801825843172229222974814626595595354080227871927084135736836982816009504513698271438428921241533814182476747433457615654262120990680451453901286737722085656689704317023028318993802925705151819971188131103795265810616802311818452495354806227139860453170462087097026164169704639022954673323576808452849810696774362089776096563624004303489021108830997313312457161613415711510200696187793117798594809441005933709736156120870473832049350332820618392052849580656761249859358995975178664031969727419138661143323098221407329057313943128190561108746058505189511214769868869437006828784716644403786293650455407308954574879631157666563955960487364090461625061946808117286500970480725120418128665786392766467538944000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
其中63代表使用n=63,而{4,3,1,1}代表在三角数序列最后四个数依次添加1,1,3,4即可。

mathe

上面代码里面还有一个极值问题没有完全介绍，也就是使用63#中放缩方案，
我们会得到一个形如\((\frac{\sum_{i=1}^n c_ix_i}{K})^K\)在约束条件\(\sum_{i=1}^nx_i=S, x_1\ge 1, x_{i+1}\ge x_i+1\)小的最值问题。
63#只介绍了如果\(c_n\)是所有系数中最大，那么我们应该让\(x_n\)尽量大即可。
但是实际计算中发现有时\(c_n\)并不是最大的，所以如果最后取到最大值，那么如果存在不同的i,j,使得\(x_{i+1}-x_i\gt 1, x_j-x{j-1}\gt 1\),而且\(c_i > c_j\), 那么我们就可以让\(x_i\)增加，\(x_j\)减少，达到总和增加的目的。也就是达到最大值时，所有大于1区间的左端点对应系数都要求不超过所有大于1区间右端点对应的系数。
所以如果存在一段区间，其左端点系数大于右端点系数的，这段区间长度必须为1。
由此我们可以先寻找\(c_i\)中逆序部分，将这些逆序部分的数进行合并，求出每个合并部分的平均值和数目（数目作为权重）。
对于合并以后的序列，我们同样可以继续寻找其中逆序部分，如果存在某个逆序部分，可以继续合并，继续求合并部分的加权平均和总数目。
反复上面过程，直到合并以后序列变成一个递增序列。这时我们只要让这个递增需要最后一项对应的那些\(x_i\)尽量大，余下部分尽量小即可。
这部分程序里面现在对应求极值部分算法还可能不对，不过应该影响不大。后续需要修正一下。

mathe

修正bug并且在验证失败时继续搜索，非常明显，遇到验证失败后，继续搜索会非常慢；如果没有遇到验证失败，会非常快。
后面可以继续考虑遇到验证失败时，如何继续剪枝

1. #include <gmpxx.h>
   
2. #include <math.h>
   
3. #include <algorithm>
   
4. #include <iostream>
   
5. 
   
6. #ifndef UB
   
7. #define UB 2025
   
8. #endif
   
9. 
   
10. int SUM;
    
11. mpz_class curbest;
    
12. int blist[UB];
    
13. int bdepth;
    
14. int bsn;
    
15. int depth;
    
16. int maxn;
    
17. int leftv;
    
18. int searchn;
    
19. int tc;
    
20. int ilist[UB];
    
21. int clist[UB];//max depth must be smaller than SUM
    
22.                //
    
23. 
    
24. void initmaxn()
    
25. {
    
26.   int h;
    
27.   leftv=0;
    
28.   for(h=1;;h++){
    
29.     if(h*(h+1)/2>SUM){
    
30.        maxn=h-1;
    
31.        leftv=SUM-maxn*(maxn+1)/2;
    
32.        return;
    
33.     }
    
34.   }
    
35. }
    
36. 
    
37. void check_last()
    
38. {
    
39.   int i,j;
    
40.   for(i=0;i<searchn;i++){
    
41.     ilist[i]=i+1;
    
42.   }
    
43.   for(i=0;i<depth;i++){
    
44.     ilist[searchn-1-i]+=clist[i];
    
45.   }
    
46.   mpz_class v=1;
    
47.   for(i=0;i<searchn;i++){
    
48.     v*=ilist[i];
    
49.     for(j=i+1;j<searchn;j++){
    
50.       v*=ilist[j]-ilist[i];
    
51.     }
    
52.   }
    
53.   tc++;
    
54.   if(v>curbest){
    
55.     curbest=v;
    
56.     bdepth=depth;
    
57. #ifdef DUMP
    
58.     std::cout<<"Found "<<tc<<" {";
    
59. #endif
    
60.     for(i=0;i<depth;i++){
    
61.       blist[i]=clist[i];
    
62. #ifdef DUMP
    
63.       std::cout<<' '<<clist[i];
    
64. #endif
    
65.     }
    
66.     bsn=searchn;
    
67. #ifdef DUMP
    
68.     std::cout<<"}: "<<curbest<<std::endl;
    
69. #endif
    
70.   }
    
71. }
    
72. 
    
73. 
    
74. void search()
    
75. {
    
76.   int i;
    
77.   int send;
    
78.   send=leftv;
    
79.   if(leftv==0){
    
80.     check_last();
    
81.     return;
    
82.   }
    
83.   if(depth>0&&send>clist[depth-1])send=clist[depth-1];
    
84.   for(i=1;i<=send;i++){
    
85.     clist[depth]=i;
    
86.     leftv-=i;
    
87.     depth++;
    
88.     if(depth<=searchn){
    
89.        search();
    
90.     }
    
91.     depth--;
    
92.     leftv+=i;
    
93.   }
    
94. }
    
95. 
    
96. mpq_class mpqpower(const mpq_class& x, int b)
    
97. {
    
98.   mpq_class p=1,m=x;
    
99.   while(b){
    
100.     if(b&1)p*=m;
     
101.     m*=m;
     
102.     b>>=1;
     
103.   }
     
104.   return p;
     
105. }
     
106. 
     
107. mpz_class intpower(int a, int b)
     
108. {
     
109.   mpz_class p=1,m=a;
     
110.   while(b){
     
111.     if(b&1)p*=m;
     
112.     m*=m;
     
113.     b>>=1;
     
114.   }
     
115.   return p;
     
116. }
     
117. 
     
118. struct WeightValue{
     
119.   int w;
     
120.   mpq_class v;
     
121. };
     
122. 
     
123. void dumpWV(WeightValue *values, int c)
     
124. {
     
125.   int i;
     
126.   for(i=0;i<c;i++){
     
127.     std::cout<<values[i].w<<':'<<values[i].v<<std::endl;
     
128.   }
     
129. }
     
130. 
     
131. void mergeSets(WeightValue *values, int& count)
     
132. {
     
133.   int i,j;
     
134.   bool increasing=false;
     
135.   while(!increasing&&count>1){
     
136.     increasing =true;
     
137.     for(i=0,j=0;i<count-1;i++){
     
138.       if(values[j].v*values[i+1].w>=values[i+1].v*values[j].w){//merge j and i+1
     
139.         values[j].v+=values[i+1].v;
     
140.         values[j].w+=values[i+1].w;
     
141.         increasing = false;
     
142.       }else{
     
143.         if(j!=i){//moves i+1 to j+1
     
144.           values[j+1].w=values[i+1].w;
     
145.           values[j+1].v=values[i+1].v;
     
146.         }
     
147.         j++;
     
148.       }
     
149.     }
     
150.     count=j+1;
     
151.   }
     
152. #ifdef DUMP
     
153.   std::cout<<"Value after merge:\n";
     
154.   dumpWV(values,count);
     
155. #endif
     
156. }
     
157. 
     
158. bool prove(int n)
     
159. {
     
160.   int i,s;
     
161.   mpq_class *onlyv=new mpq_class[n];
     
162.   WeightValue *values=new WeightValue[n];
     
163.   s=0;
     
164.   for(i=0;i<n;i++){
     
165.     clist[i]=i+1;
     
166.     s+=i+1;
     
167.   }
     
168.   int psum=SUM-s;
     
169.   while(psum>0){
     
170.     int c=(int)(sqrt(1+8*psum)+1E-10);
     
171.     c=(c-1)/2;
     
172.     if((c*(c+1))/2>psum)c--;
     
173.     for(i=0;i<c;i++){
     
174.       clist[n-1-i]+=c-i;
     
175.     }
     
176.     psum-=(c*(c+1))/2;
     
177.   }
     
178. #ifdef DUMP
     
179.   std::cout<<"Try to prove "<<n<<" using list {";
     
180.   for(i=0;i<n;i++){
     
181.     std::cout<<" "<<clist[i];
     
182.   }
     
183.   std::cout<<" }\n";
     
184. #endif
     
185.   for(i=0;i<n;i++){
     
186.     mpq_class t(1,clist[i]);
     
187.     values[i].w=1;
     
188.     values[i].v+=t;
     
189.     for(s=0;s<i;s++){
     
190.       mpq_class t(1,clist[i]-clist[s]);
     
191.       values[i].v+=t;
     
192.     }
     
193.     for(s=i+1;s<n;s++){
     
194.       mpq_class t(1,clist[s]-clist[i]);
     
195.       values[i].v-=t;
     
196.     }
     
197.     onlyv[i]=values[i].v;
     
198.   }
     
199. #ifdef DUMP
     
200.   std::cout<<"values=[";
     
201.   for(i=0;i<n;i++){
     
202.     std::cout<<" "<<values[i].v;
     
203.   }
     
204.   std::cout<<" ]\n";
     
205. #endif
     
206.   int nv=n;
     
207.   mergeSets(values,nv);
     
208. #ifdef DUMP
     
209.   std::cout<<"We need maximize value at index "<<n-values[nv-1].w+1<<std::endl;
     
210. #endif
     
211.   mpq_class fv=0;
     
212.   for(i=0;i<n-values[nv-1].w;i++){
     
213.     fv+=onlyv[i]*(i+1);
     
214.   }
     
215.   mpq_class extra(SUM-n*(n+1)/2, values[nv-1].w);
     
216.   for(i=n-values[nv-1].w;i<n;i++){
     
217.      fv+=onlyv[i]*(i+1+extra);
     
218.   }
     
219.   delete []values;
     
220.   delete []onlyv;
     
221.   fv/=n*(n+1)/2;
     
222.   fv=mpqpower(fv,n*(n+1)/2);
     
223.   mpz_class iv=1;
     
224.   for(i=0;i<n;i++){
     
225.     iv*=clist[i];
     
226.     for(s=i+1;s<n;s++){
     
227.       iv*=clist[s]-clist[i];
     
228.     }
     
229.   }
     
230.   if(fv*iv<=curbest){
     
231. #ifdef DUMP
     
232.     std::cout<<"Prove by list passed\n";
     
233. #endif
     
234.     return true;
     
235.   }else{
     
236.     std::cout<<"Prove by list failed for n="<<n<<"\n";
     
237.     return false;
     
238.   }
     
239. }
     
240. 
     
241. void check_u(int n)
     
242. {
     
243.   int i;
     
244.   mpz_class num=1, den=1;
     
245.   for(i=1;i<=n;i++){
     
246.     den*=intpower(i,i);
     
247.   }
     
248.   for(i=1;i<=n;i++){
     
249.     int v=SUM-(n-i+1)*(n-i)/2-i*(i-1)/2;
     
250.     num*=intpower(v,n-i+1);
     
251.   }
     
252.   if(num<=curbest*den){
     
253. #ifdef DUMP
     
254.     std::cout<<"U["<<SUM<<","<<n<<"] is less than best value\n";
     
255. #endif
     
256.   }else{
     
257. #ifdef DUMP
     
258.     std::cout<<"U["<<SUM<<","<<n<<"] is more than best value, more proving required\n";
     
259. #endif
     
260.     if(!prove(n)){
     
261.       searchn=n;
     
262.       leftv=SUM - n*(n+1)/2;
     
263.       std::cout<<"Search for "<<n<<" elements\n";
     
264.       search();
     
265.     }
     
266.   }
     
267. }
     
268. 
     
269. int main()
     
270. {
     
271.   int n;
     
272.   for(SUM=3;SUM<=UB;SUM++){
     
273.   initmaxn();
     
274.   searchn=maxn;
     
275. #ifdef DUMP
     
276.   std::cout<<"Max N = "<<maxn<<std::endl;
     
277. #endif
     
278.   search();
     
279. #ifdef DUMP
     
280.   std::cout<<"Total "<<tc<<" enumerated"<<std::endl;
     
281. #endif
     
282.   for(n=maxn-1;n>=1;n--){
     
283.     check_u(n);
     
284.   }
     
285. 
     
286. 
     
287.   std::cout<<SUM<<":n={0-"<<bsn<<"}+{";
     
288.   int j;
     
289.   for(j=bdepth-1;j>=0;j--){
     
290.     if(j<bdepth-1)std::cout<<",";
     
291.     std::cout<<blist[j];
     
292.   }
     
293.   std::cout<<"}\n";
     
294.   fflush(stdout);
     
295.   }
     
296.   return 0;
     
297. }
     

复制代码

已经输出的结果有(顺序搜索一个晚上到1482，被1483卡住了，可以看到后面关键都是需要继续搜索次大的n,这部分才是瓶颈)

1. 
   
2. Prove by list failed for n=1
   
3. Search for 1 elements
   
4. 3:n={0-1}+{2}
   
5. 4:n={0-2}+{1}
   
6. 5:n={0-2}+{2}
   
7. Prove by list failed for n=2
   
8. Search for 2 elements
   
9. 6:n={0-2}+{3}
   
10. 7:n={0-3}+{1}
    
11. 8:n={0-3}+{2}
    
12. 9:n={0-3}+{1,2}
    
13. Prove by list failed for n=3
    
14. Search for 3 elements
    
15. 10:n={0-3}+{1,3}
    
16. 11:n={0-4}+{1}
    
17. Prove by list failed for n=3
    
18. Search for 3 elements
    
19. 12:n={0-4}+{2}
    
20. 13:n={0-4}+{1,2}
    
21. 14:n={0-4}+{1,3}
    
22. Prove by list failed for n=4
    
23. Search for 4 elements
    
24. 15:n={0-4}+{1,4}
    
25. Prove by list failed for n=4
    
26. Search for 4 elements
    
27. 16:n={0-5}+{1}
    
28. 17:n={0-5}+{2}
    
29. 18:n={0-5}+{1,2}
    
30. 19:n={0-5}+{1,3}
    
31. Prove by list failed for n=4
    
32. Search for 4 elements
    
33. 20:n={0-5}+{1,4}
    
34. Prove by list failed for n=5
    
35. Search for 5 elements
    
36. 21:n={0-5}+{2,4}
    
37. Prove by list failed for n=5
    
38. Search for 5 elements
    
39. 22:n={0-6}+{1}
    
40. 23:n={0-6}+{2}
    
41. 24:n={0-6}+{1,2}
    
42. Prove by list failed for n=5
    
43. Search for 5 elements
    
44. 25:n={0-6}+{1,3}
    
45. 26:n={0-6}+{1,4}
    
46. 27:n={0-6}+{2,4}
    
47. Prove by list failed for n=6
    
48. Search for 6 elements
    
49. 28:n={0-6}+{1,2,4}
    
50. 29:n={0-7}+{1}
    
51. 30:n={0-7}+{2}
    
52. Prove by list failed for n=6
    
53. Search for 6 elements
    
54. 31:n={0-7}+{1,2}
    
55. 32:n={0-7}+{1,3}
    
56. 33:n={0-7}+{1,4}
    
57. 34:n={0-7}+{2,4}
    
58. 35:n={0-7}+{1,2,4}
    
59. Prove by list failed for n=7
    
60. Search for 7 elements
    
61. Prove by list failed for n=6
    
62. Search for 6 elements
    
63. 36:n={0-7}+{1,2,5}
    
64. 37:n={0-8}+{1}
    
65. Prove by list failed for n=7
    
66. Search for 7 elements
    
67. 38:n={0-8}+{2}
    
68. 39:n={0-8}+{1,2}
    
69. 40:n={0-8}+{1,3}
    
70. 41:n={0-8}+{1,4}
    
71. 42:n={0-8}+{1,2,3}
    
72. Prove by list failed for n=7
    
73. Search for 7 elements
    
74. 43:n={0-8}+{1,2,4}
    
75. 44:n={0-8}+{1,2,5}
    
76. Prove by list failed for n=8
    
77. Search for 8 elements
    
78. 45:n={0-8}+{}
    
79. Prove by list failed for n=8
    
80. Search for 8 elements
    
81. 46:n={0-9}+{1}
    
82. 47:n={0-9}+{2}
    
83. 48:n={0-9}+{1,2}
    
84. 49:n={0-9}+{1,3}
    
85. 50:n={0-9}+{1,4}
    
86. Prove by list failed for n=8
    
87. Search for 8 elements
    
88. 51:n={0-9}+{1,2,3}
    
89. 52:n={0-9}+{1,2,4}
    
90. 53:n={0-9}+{1,2,5}
    
91. 54:n={0-9}+{1,3,5}
    
92. Prove by list failed for n=9
    
93. Search for 9 elements
    
94. 55:n={0-9}+{}
    
95. 56:n={0-10}+{1}
    
96. Prove by list failed for n=8
    
97. Search for 8 elements
    
98. 57:n={0-10}+{2}
    
99. 58:n={0-10}+{1,2}
    
100. 59:n={0-10}+{1,3}
     
101. Prove by list failed for n=9
     
102. Search for 9 elements
     
103. 60:n={0-10}+{1,4}
     
104. 61:n={0-10}+{1,2,3}
     
105. 62:n={0-10}+{1,2,4}
     
106. 63:n={0-10}+{1,2,5}
     
107. 64:n={0-10}+{1,3,5}
     
108. 65:n={0-10}+{1,3,6}
     
109. Prove by list failed for n=10
     
110. Search for 10 elements
     
111. Prove by list failed for n=9
     
112. Search for 9 elements
     
113. 66:n={0-10}+{}
     
114. 67:n={0-11}+{1}
     
115. 68:n={0-11}+{2}
     
116. 69:n={0-11}+{1,2}
     
117. Prove by list failed for n=10
     
118. Search for 10 elements
     
119. 70:n={0-11}+{1,3}
     
120. 71:n={0-11}+{1,1,3}
     
121. 72:n={0-11}+{1,2,3}
     
122. 73:n={0-11}+{1,2,4}
     
123. 74:n={0-11}+{1,2,5}
     
124. 75:n={0-11}+{1,3,5}
     
125. Prove by list failed for n=10
     
126. Search for 10 elements
     
127. 76:n={0-11}+{1,3,6}
     
128. 77:n={0-11}+{1,2,3,5}
     
129. Prove by list failed for n=11
     
130. Search for 11 elements
     
131. 78:n={0-11}+{}
     
132. 79:n={0-12}+{1}
     
133. 80:n={0-12}+{2}
     
134. Prove by list failed for n=11
     
135. Search for 11 elements
     
136. 81:n={0-12}+{1,2}
     
137. 82:n={0-12}+{1,3}
     
138. 83:n={0-12}+{1,1,3}
     
139. 84:n={0-12}+{1,2,3}
     
140. 85:n={0-12}+{1,2,4}
     
141. 86:n={0-12}+{1,2,5}
     
142. Prove by list failed for n=11
     
143. Search for 11 elements
     
144. 87:n={0-12}+{1,3,5}
     
145. 88:n={0-12}+{1,1,3,5}
     
146. 89:n={0-12}+{1,2,3,5}
     
147. 90:n={0-12}+{1,2,3,6}
     
148. 91:n={0-12}+{}
     
149. 92:n={0-13}+{1}
     
150. Prove by list failed for n=12
     
151. Search for 12 elements
     
152. 93:n={0-13}+{2}
     
153. 94:n={0-13}+{1,2}
     
154. 95:n={0-13}+{1,3}
     
155. 96:n={0-13}+{1,1,3}
     
156. 97:n={0-13}+{1,2,3}
     
157. 98:n={0-13}+{1,2,4}
     
158. Prove by list failed for n=12
     
159. Search for 12 elements
     
160. 99:n={0-13}+{1,2,5}
     
161. 100:n={0-13}+{1,3,5}
     
162. 101:n={0-13}+{1,1,3,5}
     
163. 102:n={0-13}+{1,2,3,5}
     
164. 103:n={0-13}+{1,2,3,6}
     
165. 104:n={0-13}+{1,2,4,6}
     
166. Prove by list failed for n=13
     
167. Search for 13 elements
     
168. 105:n={0-13}+{}
     
169. Prove by list failed for n=13
     
170. Search for 13 elements
     
171. Prove by list failed for n=12
     
172. Search for 12 elements
     
173. 106:n={0-14}+{1}
     
174. 107:n={0-14}+{2}
     
175. 108:n={0-14}+{1,2}
     
176. 109:n={0-14}+{1,3}
     
177. 110:n={0-14}+{1,1,3}
     
178. 111:n={0-14}+{1,2,3}
     
179. Prove by list failed for n=13
     
180. Search for 13 elements
     
181. 112:n={0-14}+{1,2,4}
     
182. 113:n={0-14}+{1,2,5}
     
183. 114:n={0-14}+{1,3,5}
     
184. 115:n={0-14}+{1,1,3,5}
     
185. 116:n={0-14}+{1,2,3,5}
     
186. 117:n={0-14}+{1,2,3,6}
     
187. 118:n={0-14}+{1,2,4,6}
     
188. Prove by list failed for n=13
     
189. Search for 13 elements
     
190. 119:n={0-14}+{1,2,4,7}
     
191. Prove by list failed for n=14
     
192. Search for 14 elements
     
193. 120:n={0-14}+{}
     
194. 121:n={0-15}+{1}
     
195. 122:n={0-15}+{2}
     
196. 123:n={0-15}+{1,2}
     
197. 124:n={0-15}+{1,3}
     
198. 125:n={0-15}+{1,1,3}
     
199. Prove by list failed for n=14
     
200. Search for 14 elements
     
201. 126:n={0-15}+{1,2,3}
     
202. 127:n={0-15}+{1,2,4}
     
203. 128:n={0-15}+{1,2,5}
     
204. 129:n={0-15}+{1,3,5}
     
205. 130:n={0-15}+{1,2,3,4}
     
206. 131:n={0-15}+{1,2,3,5}
     
207. 132:n={0-15}+{1,2,3,6}
     
208. Prove by list failed for n=14
     
209. Search for 14 elements
     
210. 133:n={0-15}+{1,2,4,6}
     
211. 134:n={0-15}+{1,2,4,7}
     
212. 135:n={0-15}+{1,1,2,4,7}
     
213. 136:n={0-15}+{}
     
214. 137:n={0-16}+{1}
     
215. 138:n={0-16}+{2}
     
216. 139:n={0-16}+{1,2}
     
217. 140:n={0-16}+{1,3}
     
218. Prove by list failed for n=15
     
219. Search for 15 elements
     
220. 141:n={0-16}+{1,1,3}
     
221. 142:n={0-16}+{1,2,3}
     
222. 143:n={0-16}+{1,2,4}
     
223. 144:n={0-16}+{1,2,5}
     
224. 145:n={0-16}+{1,3,5}
     
225. 146:n={0-16}+{1,2,3,4}
     
226. 147:n={0-16}+{1,2,3,5}
     
227. Prove by list failed for n=15
     
228. Search for 15 elements
     
229. 148:n={0-16}+{1,2,3,6}
     
230. 149:n={0-16}+{1,2,4,6}
     
231. 150:n={0-16}+{1,2,4,7}
     
232. 151:n={0-16}+{1,1,2,4,7}
     
233. 152:n={0-16}+{1,2,3,4,6}
     
234. 153:n={0-16}+{}
     
235. 154:n={0-17}+{1}
     
236. 155:n={0-17}+{2}
     
237. 156:n={0-17}+{1,2}
     
238. Prove by list failed for n=16
     
239. Search for 16 elements
     
240. 157:n={0-17}+{1,3}
     
241. 158:n={0-17}+{1,1,3}
     
242. 159:n={0-17}+{1,2,3}
     
243. 160:n={0-17}+{1,2,4}
     
244. 161:n={0-17}+{1,2,5}
     
245. 162:n={0-17}+{1,3,5}
     
246. 163:n={0-17}+{1,2,3,4}
     
247. Prove by list failed for n=16
     
248. Search for 16 elements
     
249. 164:n={0-17}+{1,2,3,5}
     
250. 165:n={0-17}+{1,2,3,6}
     
251. 166:n={0-17}+{1,2,4,6}
     
252. 167:n={0-17}+{1,2,4,7}
     
253. 168:n={0-17}+{1,1,2,4,7}
     
254. 169:n={0-17}+{1,2,3,4,6}
     
255. 170:n={0-17}+{1,2,3,4,7}
     
256. 171:n={0-17}+{}
     
257. Prove by list failed for n=16
     
258. Search for 16 elements
     
259. 172:n={0-18}+{1}
     
260. 173:n={0-18}+{2}
     
261. Prove by list failed for n=17
     
262. Search for 17 elements
     
263. 174:n={0-18}+{1,2}
     
264. 175:n={0-18}+{1,3}
     
265. 176:n={0-18}+{1,1,3}
     
266. 177:n={0-18}+{1,2,3}
     
267. 178:n={0-18}+{1,2,4}
     
268. 179:n={0-18}+{1,2,5}
     
269. 180:n={0-18}+{1,3,5}
     
270. Prove by list failed for n=17
     
271. Search for 17 elements
     
272. 181:n={0-18}+{1,2,3,4}
     
273. 182:n={0-18}+{1,2,3,5}
     
274. 183:n={0-18}+{1,2,3,6}
     
275. 184:n={0-18}+{1,2,4,6}
     
276. 185:n={0-18}+{1,2,4,7}
     
277. 186:n={0-18}+{1,1,2,4,7}
     
278. 187:n={0-18}+{1,2,3,4,6}
     
279. 188:n={0-18}+{1,2,3,4,7}
     
280. Prove by list failed for n=17
     
281. Search for 17 elements
     
282. 189:n={0-18}+{1,2,3,5,7}
     
283. 190:n={0-18}+{}
     
284. 191:n={0-19}+{1}
     
285. Prove by list failed for n=18
     
286. Search for 18 elements
     
287. 192:n={0-19}+{2}
     
288. 193:n={0-19}+{1,2}
     
289. 194:n={0-19}+{1,3}
     
290. 195:n={0-19}+{1,1,3}
     
291. 196:n={0-19}+{1,2,3}
     
292. 197:n={0-19}+{1,2,4}
     
293. 198:n={0-19}+{1,2,5}
     
294. Prove by list failed for n=18
     
295. Search for 18 elements
     
296. 199:n={0-19}+{1,3,5}
     
297. 200:n={0-19}+{1,2,3,4}
     
298. 201:n={0-19}+{1,2,3,5}
     
299. 202:n={0-19}+{1,2,3,6}
     
300. 203:n={0-19}+{1,2,4,6}
     
301. 204:n={0-19}+{1,1,2,4,6}
     
302. 205:n={0-19}+{1,1,2,4,7}
     
303. 206:n={0-19}+{1,2,3,4,6}
     
304. Prove by list failed for n=18
     
305. Search for 18 elements
     
306. 207:n={0-19}+{1,2,3,4,7}
     
307. 208:n={0-19}+{1,2,3,5,7}
     
308. 209:n={0-19}+{1,2,3,5,8}
     
309. 210:n={0-19}+{}
     
310. Prove by list failed for n=19
     
311. Search for 19 elements
     
312. 211:n={0-20}+{1}
     
313. 212:n={0-20}+{2}
     
314. 213:n={0-20}+{1,2}
     
315. 214:n={0-20}+{1,3}
     
316. 215:n={0-20}+{1,1,3}
     
317. 216:n={0-20}+{1,2,3}
     
318. 217:n={0-20}+{1,2,4}
     
319. Prove by list failed for n=19
     
320. Search for 19 elements
     
321. 218:n={0-20}+{1,1,2,4}
     
322. 219:n={0-20}+{1,3,5}
     
323. 220:n={0-20}+{1,2,3,4}
     
324. 221:n={0-20}+{1,2,3,5}
     
325. 222:n={0-20}+{1,2,3,6}
     
326. 223:n={0-20}+{1,2,4,6}
     
327. 224:n={0-20}+{1,1,2,4,6}
     
328. 225:n={0-20}+{1,1,2,4,7}
     
329. Prove by list failed for n=19
     
330. Search for 19 elements
     
331. 226:n={0-20}+{1,2,3,4,6}
     
332. 227:n={0-20}+{1,2,3,4,7}
     
333. 228:n={0-20}+{1,2,3,5,7}
     
334. 229:n={0-20}+{1,2,3,5,8}
     
335. 230:n={0-20}+{1,1,2,3,5,8}
     
336. Prove by list failed for n=20
     
337. Search for 20 elements
     
338. 231:n={0-20}+{}
     
339. 232:n={0-21}+{1}
     
340. 233:n={0-21}+{2}
     
341. 234:n={0-21}+{1,2}
     
342. 235:n={0-21}+{1,3}
     
343. 236:n={0-21}+{1,1,3}
     
344. 237:n={0-21}+{1,2,3}
     
345. Prove by list failed for n=20
     
346. Search for 20 elements
     
347. 238:n={0-21}+{1,2,4}
     
348. 239:n={0-21}+{1,1,2,4}
     
349. 240:n={0-21}+{1,3,5}
     
350. 241:n={0-21}+{1,2,3,4}
     
351. 242:n={0-21}+{1,2,3,5}
     
352. 243:n={0-21}+{1,2,3,6}
     
353. 244:n={0-21}+{1,2,4,6}
     
354. 245:n={0-21}+{1,1,2,4,6}
     
355. Prove by list failed for n=20
     
356. Search for 20 elements
     
357. 246:n={0-21}+{1,1,2,4,7}
     
358. 247:n={0-21}+{1,2,3,4,6}
     
359. 248:n={0-21}+{1,2,3,4,7}
     
360. 249:n={0-21}+{1,2,3,5,7}
     
361. 250:n={0-21}+{1,2,3,5,8}
     
362. 251:n={0-21}+{1,1,2,3,5,8}
     
363. 252:n={0-21}+{1,1,2,4,5,8}
     
364. 253:n={0-21}+{}
     
365. 254:n={0-22}+{1}
     
366. 255:n={0-22}+{2}
     
367. 256:n={0-22}+{1,2}
     
368. 257:n={0-22}+{1,3}
     
369. 258:n={0-22}+{1,1,3}
     
370. Prove by list failed for n=21
     
371. Search for 21 elements
     
372. 259:n={0-22}+{1,2,3}
     
373. 260:n={0-22}+{1,2,4}
     
374. 261:n={0-22}+{1,1,2,4}
     
375. 262:n={0-22}+{1,3,5}
     
376. 263:n={0-22}+{1,2,3,4}
     
377. 264:n={0-22}+{1,2,3,5}
     
378. 265:n={0-22}+{1,2,3,6}
     
379. 266:n={0-22}+{1,2,4,6}
     
380. Prove by list failed for n=21
     
381. Search for 21 elements
     
382. 267:n={0-22}+{1,1,2,4,6}
     
383. 268:n={0-22}+{1,1,2,4,7}
     
384. 269:n={0-22}+{1,2,3,4,6}
     
385. 270:n={0-22}+{1,2,3,4,7}
     
386. 271:n={0-22}+{1,2,3,5,7}
     
387. 272:n={0-22}+{1,2,3,5,8}
     
388. 273:n={0-22}+{1,1,2,3,5,8}
     
389. 274:n={0-22}+{1,1,2,4,5,8}
     
390. 275:n={0-22}+{1,1,2,4,6,8}
     
391. 276:n={0-22}+{}
     
392. 277:n={0-23}+{1}
     
393. 278:n={0-23}+{2}
     
394. 279:n={0-23}+{1,2}
     
395. 280:n={0-23}+{1,3}
     
396. Prove by list failed for n=22
     
397. Search for 22 elements
     
398. 281:n={0-23}+{1,1,3}
     
399. 282:n={0-23}+{1,2,3}
     
400. 283:n={0-23}+{1,2,4}
     
401. 284:n={0-23}+{1,1,2,4}
     
402. 285:n={0-23}+{1,1,3,4}
     
403. 286:n={0-23}+{1,2,3,4}
     
404. 287:n={0-23}+{1,2,3,5}
     
405. 288:n={0-23}+{1,2,3,6}
     
406. Prove by list failed for n=22
     
407. Search for 22 elements
     
408. 289:n={0-23}+{1,2,4,6}
     
409. 290:n={0-23}+{1,1,2,4,6}
     
410. 291:n={0-23}+{1,1,3,4,6}
     
411. 292:n={0-23}+{1,2,3,4,6}
     
412. 293:n={0-23}+{1,2,3,4,7}
     
413. 294:n={0-23}+{1,2,3,5,7}
     
414. 295:n={0-23}+{1,2,3,5,8}
     
415. 296:n={0-23}+{1,1,2,3,5,8}
     
416. 297:n={0-23}+{1,1,2,4,5,8}
     
417. Prove by list failed for n=22
     
418. Search for 22 elements
     
419. 298:n={0-23}+{1,1,2,4,6,8}
     
420. 299:n={0-23}+{1,2,3,4,5,8}
     
421. 300:n={0-23}+{}
     
422. 301:n={0-24}+{1}
     
423. 302:n={0-24}+{2}
     
424. 303:n={0-24}+{1,2}
     
425. Prove by list failed for n=23
     
426. Search for 23 elements
     
427. 304:n={0-24}+{1,3}
     
428. 305:n={0-24}+{1,1,3}
     
429. 306:n={0-24}+{1,2,3}
     
430. 307:n={0-24}+{1,2,4}
     
431. 308:n={0-24}+{1,1,2,4}
     
432. 309:n={0-24}+{1,1,3,4}
     
433. 310:n={0-24}+{1,2,3,4}
     
434. 311:n={0-24}+{1,2,3,5}
     
435. Prove by list failed for n=23
     
436. Search for 23 elements
     
437. 312:n={0-24}+{1,2,3,6}
     
438. 313:n={0-24}+{1,2,4,6}
     
439. 314:n={0-24}+{1,1,2,4,6}
     
440. 315:n={0-24}+{1,1,3,4,6}
     
441. 316:n={0-24}+{1,2,3,4,6}
     
442. 317:n={0-24}+{1,2,3,4,7}
     
443. 318:n={0-24}+{1,2,3,5,7}
     
444. 319:n={0-24}+{1,2,3,5,8}
     
445. 320:n={0-24}+{1,1,2,3,5,8}
     
446. Prove by list failed for n=23
     
447. Search for 23 elements
     
448. 321:n={0-24}+{1,1,2,4,5,8}
     
449. 322:n={0-24}+{1,2,3,4,5,7}
     
450. 323:n={0-24}+{1,2,3,4,5,8}
     
451. 324:n={0-24}+{1,2,3,4,6,8}
     
452. 325:n={0-24}+{}
     
453. 326:n={0-25}+{1}
     
454. 327:n={0-25}+{2}
     
455. Prove by list failed for n=24
     
456. Search for 24 elements
     
457. 328:n={0-25}+{1,2}
     
458. 329:n={0-25}+{1,3}
     
459. 330:n={0-25}+{1,1,3}
     
460. 331:n={0-25}+{1,2,3}
     
461. 332:n={0-25}+{1,2,4}
     
462. 333:n={0-25}+{1,1,2,4}
     
463. 334:n={0-25}+{1,1,3,4}
     
464. 335:n={0-25}+{1,2,3,4}
     
465. Prove by list failed for n=24
     
466. Search for 24 elements
     
467. 336:n={0-25}+{1,2,3,5}
     
468. 337:n={0-25}+{1,2,3,6}
     
469. 338:n={0-25}+{1,2,4,6}
     
470. 339:n={0-25}+{1,1,2,4,6}
     
471. 340:n={0-25}+{1,1,3,4,6}
     
472. 341:n={0-25}+{1,2,3,4,6}
     
473. 342:n={0-25}+{1,2,3,4,7}
     
474. 343:n={0-25}+{1,2,3,5,7}
     
475. 344:n={0-25}+{1,1,2,3,5,7}
     
476. Prove by list failed for n=24
     
477. Search for 24 elements
     
478. 345:n={0-25}+{1,1,2,3,5,8}
     
479. 346:n={0-25}+{1,1,2,4,5,8}
     
480. 347:n={0-25}+{1,2,3,4,5,7}
     
481. 348:n={0-25}+{1,2,3,4,5,8}
     
482. 349:n={0-25}+{1,2,3,4,6,8}
     
483. 350:n={0-25}+{1,2,3,4,6,9}
     
484. 351:n={0-25}+{}
     
485. 352:n={0-26}+{1}
     
486. Prove by list failed for n=25
     
487. Search for 25 elements
     
488. 353:n={0-26}+{2}
     
489. 354:n={0-26}+{1,2}
     
490. 355:n={0-26}+{1,3}
     
491. 356:n={0-26}+{1,1,3}
     
492. 357:n={0-26}+{1,2,3}
     
493. 358:n={0-26}+{1,2,4}
     
494. 359:n={0-26}+{1,1,2,4}
     
495. 360:n={0-26}+{1,1,3,4}
     
496. Prove by list failed for n=25
     
497. Search for 25 elements
     
498. 361:n={0-26}+{1,2,3,4}
     
499. 362:n={0-26}+{1,2,3,5}
     
500. 363:n={0-26}+{1,2,3,6}
     
501. 364:n={0-26}+{1,2,4,6}
     
502. 365:n={0-26}+{1,1,2,4,6}
     
503. 366:n={0-26}+{1,1,3,4,6}
     
504. 367:n={0-26}+{1,2,3,4,6}
     
505. 368:n={0-26}+{1,2,3,4,7}
     
506. 369:n={0-26}+{1,2,3,5,7}
     
507. Prove by list failed for n=25
     
508. Search for 25 elements
     
509. 370:n={0-26}+{1,1,2,3,5,7}
     
510. 371:n={0-26}+{1,1,2,3,5,8}
     
511. 372:n={0-26}+{1,1,2,4,5,8}
     
512. 373:n={0-26}+{1,2,3,4,5,7}
     
513. 374:n={0-26}+{1,2,3,4,5,8}
     
514. 375:n={0-26}+{1,2,3,4,6,8}
     
515. 376:n={0-26}+{1,2,3,4,6,9}
     
516. 377:n={0-26}+{1,1,2,3,4,6,9}
     
517. 378:n={0-26}+{}
     
518. Prove by list failed for n=26
     
519. Search for 26 elements
     
520. 379:n={0-27}+{1}
     
521. 380:n={0-27}+{2}
     
522. 381:n={0-27}+{1,2}
     
523. 382:n={0-27}+{1,3}
     
524. 383:n={0-27}+{1,1,3}
     
525. 384:n={0-27}+{1,2,3}
     
526. 385:n={0-27}+{1,2,4}
     
527. 386:n={0-27}+{1,1,2,4}
     
528. Prove by list failed for n=26
     
529. Search for 26 elements
     
530. 387:n={0-27}+{1,1,3,4}
     
531. 388:n={0-27}+{1,2,3,4}
     
532. 389:n={0-27}+{1,2,3,5}
     
533. 390:n={0-27}+{1,2,3,6}
     
534. 391:n={0-27}+{1,2,4,6}
     
535. 392:n={0-27}+{1,1,2,4,6}
     
536. 393:n={0-27}+{1,1,3,4,6}
     
537. 394:n={0-27}+{1,2,3,4,6}
     
538. 395:n={0-27}+{1,2,3,4,7}
     
539. Prove by list failed for n=26
     
540. Search for 26 elements
     
541. 396:n={0-27}+{1,2,3,5,7}
     
542. 397:n={0-27}+{1,1,2,3,5,7}
     
543. 398:n={0-27}+{1,1,2,3,5,8}
     
544. 399:n={0-27}+{1,1,2,4,5,8}
     
545. 400:n={0-27}+{1,2,3,4,5,7}
     
546. 401:n={0-27}+{1,2,3,4,5,8}
     
547. 402:n={0-27}+{1,2,3,4,6,8}
     
548. 403:n={0-27}+{1,2,3,4,6,9}
     
549. 404:n={0-27}+{1,1,2,3,4,6,9}
     
550. 405:n={0-27}+{1,1,2,3,5,6,9}
     
551. Prove by list failed for n=27
     
552. Search for 27 elements
     
553. 406:n={0-27}+{}
     
554. 407:n={0-28}+{1}
     
555. 408:n={0-28}+{2}
     
556. 409:n={0-28}+{1,2}
     
557. 410:n={0-28}+{1,3}
     
558. 411:n={0-28}+{1,1,3}
     
559. 412:n={0-28}+{1,2,3}
     
560. 413:n={0-28}+{1,2,4}
     
561. Prove by list failed for n=27
     
562. Search for 27 elements
     
563. 414:n={0-28}+{1,1,2,4}
     
564. 415:n={0-28}+{1,1,3,4}
     
565. 416:n={0-28}+{1,2,3,4}
     
566. 417:n={0-28}+{1,2,3,5}
     
567. 418:n={0-28}+{1,1,2,3,5}
     
568. 419:n={0-28}+{1,2,4,6}
     
569. 420:n={0-28}+{1,1,2,4,6}
     
570. 421:n={0-28}+{1,2,3,4,5}
     
571. 422:n={0-28}+{1,2,3,4,6}
     
572. Prove by list failed for n=27
     
573. Search for 27 elements
     
574. 423:n={0-28}+{1,2,3,4,7}
     
575. 424:n={0-28}+{1,2,3,5,7}
     
576. 425:n={0-28}+{1,1,2,3,5,7}
     
577. 426:n={0-28}+{1,1,2,3,5,8}
     
578. 427:n={0-28}+{1,1,2,4,5,8}
     
579. 428:n={0-28}+{1,2,3,4,5,7}
     
580. 429:n={0-28}+{1,2,3,4,5,8}
     
581. 430:n={0-28}+{1,2,3,4,6,8}
     
582. 431:n={0-28}+{1,2,3,4,6,9}
     
583. 432:n={0-28}+{1,1,2,3,4,6,9}
     
584. Prove by list failed for n=27
     
585. Search for 27 elements
     
586. 433:n={0-28}+{1,1,2,3,5,6,9}
     
587. 434:n={0-28}+{1,1,2,3,5,7,9}
     
588. 435:n={0-28}+{}
     
589. 436:n={0-29}+{1}
     
590. 437:n={0-29}+{2}
     
591. 438:n={0-29}+{1,2}
     
592. 439:n={0-29}+{1,3}
     
593. 440:n={0-29}+{1,1,3}
     
594. 441:n={0-29}+{1,2,3}
     
595. Prove by list failed for n=28
     
596. Search for 28 elements
     
597. 442:n={0-29}+{1,2,4}
     
598. 443:n={0-29}+{1,1,2,4}
     
599. 444:n={0-29}+{1,1,3,4}
     
600. 445:n={0-29}+{1,2,3,4}
     
601. 446:n={0-29}+{1,2,3,5}
     
602. 447:n={0-29}+{1,1,2,3,5}
     
603. 448:n={0-29}+{1,2,4,6}
     
604. 449:n={0-29}+{1,1,2,4,6}
     
605. 450:n={0-29}+{1,2,3,4,5}
     
606. Prove by list failed for n=28
     
607. Search for 28 elements
     
608. 451:n={0-29}+{1,2,3,4,6}
     
609. 452:n={0-29}+{1,2,3,4,7}
     
610. 453:n={0-29}+{1,2,3,5,7}
     
611. 454:n={0-29}+{1,1,2,3,5,7}
     
612. 455:n={0-29}+{1,1,2,3,5,8}
     
613. 456:n={0-29}+{1,1,2,4,5,8}
     
614. 457:n={0-29}+{1,2,3,4,5,7}
     
615. 458:n={0-29}+{1,2,3,4,5,8}
     
616. 459:n={0-29}+{1,2,3,4,6,8}
     
617. 460:n={0-29}+{1,2,3,4,6,9}
     
618. Prove by list failed for n=28
     
619. Search for 28 elements
     
620. 461:n={0-29}+{1,1,2,3,4,6,9}
     
621. 462:n={0-29}+{1,1,2,3,5,6,9}
     
622. 463:n={0-29}+{1,1,2,3,5,7,9}
     
623. 464:n={0-29}+{1,1,2,3,5,7,10}
     
624. 465:n={0-29}+{}
     
625. 466:n={0-30}+{1}
     
626. 467:n={0-30}+{2}
     
627. 468:n={0-30}+{1,2}
     
628. 469:n={0-30}+{1,3}
     
629. 470:n={0-30}+{1,1,3}
     
630. Prove by list failed for n=29
     
631. Search for 29 elements
     
632. 471:n={0-30}+{1,2,3}
     
633. 472:n={0-30}+{1,2,4}
     
634. 473:n={0-30}+{1,1,2,4}
     
635. 474:n={0-30}+{1,1,3,4}
     
636. 475:n={0-30}+{1,2,3,4}
     
637. 476:n={0-30}+{1,2,3,5}
     
638. 477:n={0-30}+{1,1,2,3,5}
     
639. 478:n={0-30}+{1,2,4,6}
     
640. 479:n={0-30}+{1,1,2,4,6}
     
641. Prove by list failed for n=29
     
642. Search for 29 elements
     
643. 480:n={0-30}+{1,2,3,4,5}
     
644. 481:n={0-30}+{1,2,3,4,6}
     
645. 482:n={0-30}+{1,2,3,4,7}
     
646. 483:n={0-30}+{1,2,3,5,7}
     
647. 484:n={0-30}+{1,1,2,3,5,7}
     
648. 485:n={0-30}+{1,1,2,3,5,8}
     
649. 486:n={0-30}+{1,1,2,4,5,8}
     
650. 487:n={0-30}+{1,2,3,4,5,7}
     
651. 488:n={0-30}+{1,2,3,4,5,8}
     
652. 489:n={0-30}+{1,2,3,4,6,8}
     
653. Prove by list failed for n=29
     
654. Search for 29 elements
     
655. 490:n={0-30}+{1,2,3,4,6,9}
     
656. 491:n={0-30}+{1,1,2,3,4,6,9}
     
657. 492:n={0-30}+{1,1,2,3,5,6,9}
     
658. 493:n={0-30}+{1,1,2,3,5,7,9}
     
659. 494:n={0-30}+{1,1,2,3,5,7,10}
     
660. 495:n={0-30}+{1,2,3,4,5,6,9}
     
661. 496:n={0-30}+{}
     
662. 497:n={0-31}+{1}
     
663. 498:n={0-31}+{2}
     
664. 499:n={0-31}+{1,2}
     
665. 500:n={0-31}+{1,3}
     
666. Prove by list failed for n=30
     
667. Search for 30 elements
     
668. 501:n={0-31}+{1,1,3}
     
669. 502:n={0-31}+{1,2,3}
     
670. 503:n={0-31}+{1,2,4}
     
671. 504:n={0-31}+{1,1,2,4}
     
672. 505:n={0-31}+{1,1,3,4}
     
673. 506:n={0-31}+{1,2,3,4}
     
674. 507:n={0-31}+{1,2,3,5}
     
675. 508:n={0-31}+{1,1,2,3,5}
     
676. 509:n={0-31}+{1,2,4,6}
     
677. Prove by list failed for n=30
     
678. Search for 30 elements
     
679. 510:n={0-31}+{1,1,2,4,6}
     
680. 511:n={0-31}+{1,2,3,4,5}
     
681. 512:n={0-31}+{1,2,3,4,6}
     
682. 513:n={0-31}+{1,2,3,4,7}
     
683. 514:n={0-31}+{1,2,3,5,7}
     
684. 515:n={0-31}+{1,1,2,3,5,7}
     
685. 516:n={0-31}+{1,1,2,3,5,8}
     
686. 517:n={0-31}+{1,1,2,4,5,8}
     
687. 518:n={0-31}+{1,2,3,4,5,7}
     
688. 519:n={0-31}+{1,2,3,4,5,8}
     
689. Prove by list failed for n=30
     
690. Search for 30 elements
     
691. 520:n={0-31}+{1,2,3,4,6,8}
     
692. 521:n={0-31}+{1,1,2,3,4,6,8}
     
693. 522:n={0-31}+{1,1,2,3,4,6,9}
     
694. 523:n={0-31}+{1,1,2,3,5,6,9}
     
695. 524:n={0-31}+{1,1,2,3,5,7,9}
     
696. 525:n={0-31}+{1,1,2,3,5,7,10}
     
697. 526:n={0-31}+{1,2,3,4,5,6,9}
     
698. 527:n={0-31}+{1,2,3,4,5,7,9}
     
699. 528:n={0-31}+{}
     
700. 529:n={0-32}+{1}
     
701. 530:n={0-32}+{2}
     
702. 531:n={0-32}+{1,2}
     
703. Prove by list failed for n=31
     
704. Search for 31 elements
     
705. 532:n={0-32}+{1,3}
     
706. 533:n={0-32}+{1,1,3}
     
707. 534:n={0-32}+{1,2,3}
     
708. 535:n={0-32}+{1,2,4}
     
709. 536:n={0-32}+{1,1,2,4}
     
710. 537:n={0-32}+{1,1,3,4}
     
711. 538:n={0-32}+{1,2,3,4}
     
712. 539:n={0-32}+{1,2,3,5}
     
713. 540:n={0-32}+{1,1,2,3,5}
     
714. Prove by list failed for n=31
     
715. Search for 31 elements
     
716. 541:n={0-32}+{1,2,4,6}
     
717. 542:n={0-32}+{1,1,2,4,6}
     
718. 543:n={0-32}+{1,2,3,4,5}
     
719. 544:n={0-32}+{1,2,3,4,6}
     
720. 545:n={0-32}+{1,2,3,4,7}
     
721. 546:n={0-32}+{1,2,3,5,7}
     
722. 547:n={0-32}+{1,1,2,3,5,7}
     
723. 548:n={0-32}+{1,1,2,3,5,8}
     
724. 549:n={0-32}+{1,1,2,4,5,8}
     
725. 550:n={0-32}+{1,2,3,4,5,7}
     
726. Prove by list failed for n=31
     
727. Search for 31 elements
     
728. 551:n={0-32}+{1,2,3,4,5,8}
     
729. 552:n={0-32}+{1,2,3,4,6,8}
     
730. 553:n={0-32}+{1,1,2,3,4,6,8}
     
731. 554:n={0-32}+{1,1,2,3,4,6,9}
     
732. 555:n={0-32}+{1,1,2,3,5,6,9}
     
733. 556:n={0-32}+{1,1,2,3,5,7,9}
     
734. 557:n={0-32}+{1,1,2,3,5,7,10}
     
735. 558:n={0-32}+{1,2,3,4,5,6,9}
     
736. 559:n={0-32}+{1,2,3,4,5,7,9}
     
737. 560:n={0-32}+{1,2,3,4,5,7,10}
     
738. 561:n={0-32}+{}
     
739. 562:n={0-33}+{1}
     
740. 563:n={0-33}+{2}
     
741. Prove by list failed for n=32
     
742. Search for 32 elements
     
743. 564:n={0-33}+{1,2}
     
744. 565:n={0-33}+{1,3}
     
745. 566:n={0-33}+{1,1,3}
     
746. 567:n={0-33}+{1,2,3}
     
747. 568:n={0-33}+{1,2,4}
     
748. 569:n={0-33}+{1,1,2,4}
     
749. 570:n={0-33}+{1,1,3,4}
     
750. 571:n={0-33}+{1,2,3,4}
     
751. 572:n={0-33}+{1,2,3,5}
     
752. Prove by list failed for n=32
     
753. Search for 32 elements
     
754. 573:n={0-33}+{1,1,2,3,5}
     
755. 574:n={0-33}+{1,1,2,3,6}
     
756. 575:n={0-33}+{1,1,2,4,6}
     
757. 576:n={0-33}+{1,2,3,4,5}
     
758. 577:n={0-33}+{1,2,3,4,6}
     
759. 578:n={0-33}+{1,2,3,4,7}
     
760. 579:n={0-33}+{1,2,3,5,7}
     
761. 580:n={0-33}+{1,1,2,3,5,7}
     
762. 581:n={0-33}+{1,1,2,3,5,8}
     
763. 582:n={0-33}+{1,1,2,4,5,8}
     
764. Prove by list failed for n=32
     
765. Search for 32 elements
     
766. 583:n={0-33}+{1,2,3,4,5,7}
     
767. 584:n={0-33}+{1,2,3,4,5,8}
     
768. 585:n={0-33}+{1,2,3,4,6,8}
     
769. 586:n={0-33}+{1,1,2,3,4,6,8}
     
770. 587:n={0-33}+{1,1,2,3,4,6,9}
     
771. 588:n={0-33}+{1,1,2,3,5,6,9}
     
772. 589:n={0-33}+{1,1,2,3,5,7,9}
     
773. 590:n={0-33}+{1,1,2,3,5,7,10}
     
774. 591:n={0-33}+{1,2,3,4,5,6,9}
     
775. 592:n={0-33}+{1,2,3,4,5,7,9}
     
776. 593:n={0-33}+{1,2,3,4,5,7,10}
     
777. Prove by list failed for n=32
     
778. Search for 32 elements
     
779. 594:n={0-33}+{1,1,2,3,4,5,7,10}
     
780. 595:n={0-33}+{}
     
781. 596:n={0-34}+{1}
     
782. Prove by list failed for n=33
     
783. Search for 33 elements
     
784. 597:n={0-34}+{2}
     
785. 598:n={0-34}+{1,2}
     
786. 599:n={0-34}+{1,3}
     
787. 600:n={0-34}+{1,1,3}
     
788. 601:n={0-34}+{1,2,3}
     
789. 602:n={0-34}+{1,2,4}
     
790. 603:n={0-34}+{1,1,2,4}
     
791. 604:n={0-34}+{1,1,3,4}
     
792. 605:n={0-34}+{1,2,3,4}
     
793. Prove by list failed for n=33
     
794. Search for 33 elements
     
795. 606:n={0-34}+{1,2,3,5}
     
796. 607:n={0-34}+{1,1,2,3,5}
     
797. 608:n={0-34}+{1,1,2,3,6}
     
798. 609:n={0-34}+{1,1,2,4,6}
     
799. 610:n={0-34}+{1,2,3,4,5}
     
800. 611:n={0-34}+{1,2,3,4,6}
     
801. 612:n={0-34}+{1,2,3,4,7}
     
802. 613:n={0-34}+{1,2,3,5,7}
     
803. 614:n={0-34}+{1,1,2,3,5,7}
     
804. 615:n={0-34}+{1,1,2,3,5,8}
     
805. Prove by list failed for n=33
     
806. Search for 33 elements
     
807. 616:n={0-34}+{1,1,2,4,5,8}
     
808. 617:n={0-34}+{1,2,3,4,5,7}
     
809. 618:n={0-34}+{1,2,3,4,5,8}
     
810. 619:n={0-34}+{1,2,3,4,6,8}
     
811. 620:n={0-34}+{1,1,2,3,4,6,8}
     
812. 621:n={0-34}+{1,1,2,3,4,6,9}
     
813. 622:n={0-34}+{1,1,2,3,5,6,9}
     
814. 623:n={0-34}+{1,1,2,3,5,7,9}
     
815. 624:n={0-34}+{1,1,2,3,5,7,10}
     
816. 625:n={0-34}+{1,2,3,4,5,6,9}
     
817. 626:n={0-34}+{1,2,3,4,5,7,9}
     
818. Prove by list failed for n=33
     
819. Search for 33 elements
     
820. 627:n={0-34}+{1,2,3,4,5,7,10}
     
821. 628:n={0-34}+{1,1,2,3,4,5,7,10}
     
822. 629:n={0-34}+{1,1,2,3,4,6,7,10}
     
823. 630:n={0-34}+{}
     
824. Prove by list failed for n=34
     
825. Search for 34 elements
     
826. 631:n={0-35}+{1}
     
827. 632:n={0-35}+{2}
     
828. 633:n={0-35}+{1,2}
     
829. 634:n={0-35}+{1,3}
     
830. 635:n={0-35}+{1,1,3}
     
831. 636:n={0-35}+{1,2,3}
     
832. 637:n={0-35}+{1,2,4}
     
833. 638:n={0-35}+{1,1,2,4}
     
834. 639:n={0-35}+{1,1,3,4}
     
835. 640:n={0-35}+{1,2,3,4}
     
836. 641:n={0-35}+{1,2,3,5}
     
837. 642:n={0-35}+{1,1,2,3,5}
     
838. 643:n={0-35}+{1,1,2,3,6}
     
839. 644:n={0-35}+{1,1,2,4,6}
     
840. 645:n={0-35}+{1,2,3,4,5}
     
841. 646:n={0-35}+{1,2,3,4,6}
     
842. 647:n={0-35}+{1,2,3,4,7}
     
843. 648:n={0-35}+{1,2,3,5,7}
     
844. 649:n={0-35}+{1,1,2,3,5,7}
     
845. Prove by list failed for n=34
     
846. Search for 34 elements
     
847. 650:n={0-35}+{1,1,2,3,5,8}
     
848. 651:n={0-35}+{1,1,2,4,5,8}
     
849. 652:n={0-35}+{1,2,3,4,5,7}
     
850. 653:n={0-35}+{1,2,3,4,5,8}
     
851. 654:n={0-35}+{1,2,3,4,6,8}
     
852. 655:n={0-35}+{1,1,2,3,4,6,8}
     
853. 656:n={0-35}+{1,1,2,3,4,6,9}
     
854. 657:n={0-35}+{1,1,2,3,5,6,9}
     
855. 658:n={0-35}+{1,1,2,3,5,7,9}
     
856. 659:n={0-35}+{1,1,2,3,5,7,10}
     
857. 660:n={0-35}+{1,2,3,4,5,6,9}
     
858. Prove by list failed for n=34
     
859. Search for 34 elements
     
860. 661:n={0-35}+{1,2,3,4,5,7,9}
     
861. 662:n={0-35}+{1,2,3,4,5,7,10}
     
862. 663:n={0-35}+{1,1,2,3,4,5,7,10}
     
863. 664:n={0-35}+{1,1,2,3,4,6,7,10}
     
864. 665:n={0-35}+{1,1,2,3,4,6,8,10}
     
865. Prove by list failed for n=35
     
866. Search for 35 elements
     
867. 666:n={0-35}+{}
     
868. 667:n={0-36}+{1}
     
869. 668:n={0-36}+{2}
     
870. 669:n={0-36}+{1,2}
     
871. 670:n={0-36}+{1,3}
     
872. 671:n={0-36}+{1,1,3}
     
873. 672:n={0-36}+{1,2,3}
     
874. 673:n={0-36}+{1,2,4}
     
875. 674:n={0-36}+{1,1,2,4}
     
876. 675:n={0-36}+{1,1,3,4}
     
877. 676:n={0-36}+{1,2,3,4}
     
878. 677:n={0-36}+{1,2,3,5}
     
879. 678:n={0-36}+{1,1,2,3,5}
     
880. 679:n={0-36}+{1,1,2,3,6}
     
881. 680:n={0-36}+{1,1,2,4,6}
     
882. 681:n={0-36}+{1,2,3,4,5}
     
883. 682:n={0-36}+{1,2,3,4,6}
     
884. 683:n={0-36}+{1,1,2,3,4,6}
     
885. 684:n={0-36}+{1,2,3,5,7}
     
886. Prove by list failed for n=35
     
887. Search for 35 elements
     
888. 685:n={0-36}+{1,1,2,3,5,7}
     
889. 686:n={0-36}+{1,1,2,3,5,8}
     
890. 687:n={0-36}+{1,1,2,4,5,8}
     
891. 688:n={0-36}+{1,2,3,4,5,7}
     
892. 689:n={0-36}+{1,2,3,4,5,8}
     
893. 690:n={0-36}+{1,2,3,4,6,8}
     
894. 691:n={0-36}+{1,1,2,3,4,6,8}
     
895. 692:n={0-36}+{1,1,2,3,4,6,9}
     
896. 693:n={0-36}+{1,1,2,3,5,6,9}
     
897. 694:n={0-36}+{1,1,2,3,5,7,9}
     
898. 695:n={0-36}+{1,1,2,3,5,7,10}
     
899. Prove by list failed for n=35
     
900. Search for 35 elements
     
901. 696:n={0-36}+{1,2,3,4,5,6,9}
     
902. 697:n={0-36}+{1,2,3,4,5,7,9}
     
903. 698:n={0-36}+{1,2,3,4,5,7,10}
     
904. 699:n={0-36}+{1,1,2,3,4,5,7,10}
     
905. 700:n={0-36}+{1,1,2,3,4,6,7,10}
     
906. 701:n={0-36}+{1,1,2,3,4,6,8,10}
     
907. 702:n={0-36}+{1,1,2,3,4,6,8,11}
     
908. 703:n={0-36}+{}
     
909. 704:n={0-37}+{1}
     
910. 705:n={0-37}+{2}
     
911. 706:n={0-37}+{1,2}
     
912. 707:n={0-37}+{1,3}
     
913. 708:n={0-37}+{1,1,3}
     
914. 709:n={0-37}+{1,2,3}
     
915. 710:n={0-37}+{1,2,4}
     
916. 711:n={0-37}+{1,1,2,4}
     
917. 712:n={0-37}+{1,1,3,4}
     
918. 713:n={0-37}+{1,2,3,4}
     
919. 714:n={0-37}+{1,2,3,5}
     
920. 715:n={0-37}+{1,1,2,3,5}
     
921. 716:n={0-37}+{1,1,2,3,6}
     
922. 717:n={0-37}+{1,1,2,4,6}
     
923. 718:n={0-37}+{1,2,3,4,5}
     
924. 719:n={0-37}+{1,2,3,4,6}
     
925. 720:n={0-37}+{1,1,2,3,4,6}
     
926. Prove by list failed for n=36
     
927. Search for 36 elements
     
928. 721:n={0-37}+{1,2,3,5,7}
     
929. 722:n={0-37}+{1,1,2,3,5,7}
     
930. 723:n={0-37}+{1,1,2,3,5,8}
     
931. 724:n={0-37}+{1,1,2,4,5,8}
     
932. 725:n={0-37}+{1,2,3,4,5,7}
     
933. 726:n={0-37}+{1,2,3,4,5,8}
     
934. 727:n={0-37}+{1,2,3,4,6,8}
     
935. 728:n={0-37}+{1,1,2,3,4,6,8}
     
936. 729:n={0-37}+{1,1,2,3,4,6,9}
     
937. 730:n={0-37}+{1,1,2,3,5,6,9}
     
938. 731:n={0-37}+{1,1,2,3,5,7,9}
     
939. Prove by list failed for n=36
     
940. Search for 36 elements
     
941. 732:n={0-37}+{1,1,2,3,5,7,10}
     
942. 733:n={0-37}+{1,2,3,4,5,6,9}
     
943. 734:n={0-37}+{1,2,3,4,5,7,9}
     
944. 735:n={0-37}+{1,1,2,3,4,5,7,9}
     
945. 736:n={0-37}+{1,1,2,3,4,5,7,10}
     
946. 737:n={0-37}+{1,1,2,3,4,6,7,10}
     
947. 738:n={0-37}+{1,1,2,3,4,6,8,10}
     
948. 739:n={0-37}+{1,1,2,3,4,6,8,11}
     
949. 740:n={0-37}+{1,1,2,3,5,6,8,11}
     
950. 741:n={0-37}+{}
     
951. 742:n={0-38}+{1}
     
952. 743:n={0-38}+{2}
     
953. 744:n={0-38}+{1,2}
     
954. 745:n={0-38}+{1,3}
     
955. 746:n={0-38}+{1,1,3}
     
956. 747:n={0-38}+{1,2,3}
     
957. 748:n={0-38}+{1,2,4}
     
958. 749:n={0-38}+{1,1,2,4}
     
959. 750:n={0-38}+{1,1,3,4}
     
960. 751:n={0-38}+{1,2,3,4}
     
961. 752:n={0-38}+{1,2,3,5}
     
962. 753:n={0-38}+{1,1,2,3,5}
     
963. 754:n={0-38}+{1,1,2,3,6}
     
964. 755:n={0-38}+{1,1,2,4,6}
     
965. 756:n={0-38}+{1,2,3,4,5}
     
966. 757:n={0-38}+{1,2,3,4,6}
     
967. Prove by list failed for n=37
     
968. Search for 37 elements
     
969. 758:n={0-38}+{1,1,2,3,4,6}
     
970. 759:n={0-38}+{1,2,3,5,7}
     
971. 760:n={0-38}+{1,1,2,3,5,7}
     
972. 761:n={0-38}+{1,1,2,3,5,8}
     
973. 762:n={0-38}+{1,1,2,4,5,8}
     
974. 763:n={0-38}+{1,2,3,4,5,7}
     
975. 764:n={0-38}+{1,2,3,4,5,8}
     
976. 765:n={0-38}+{1,2,3,4,6,8}
     
977. 766:n={0-38}+{1,1,2,3,4,6,8}
     
978. 767:n={0-38}+{1,1,2,3,4,6,9}
     
979. 768:n={0-38}+{1,1,2,3,5,6,9}
     
980. Prove by list failed for n=37
     
981. Search for 37 elements
     
982. 769:n={0-38}+{1,1,2,3,5,7,9}
     
983. 770:n={0-38}+{1,1,2,3,5,7,10}
     
984. 771:n={0-38}+{1,2,3,4,5,6,9}
     
985. 772:n={0-38}+{1,2,3,4,5,7,9}
     
986. 773:n={0-38}+{1,1,2,3,4,5,7,9}
     
987. 774:n={0-38}+{1,1,2,3,4,5,7,10}
     
988. 775:n={0-38}+{1,1,2,3,4,6,7,10}
     
989. 776:n={0-38}+{1,1,2,3,4,6,8,10}
     
990. 777:n={0-38}+{1,1,2,3,4,6,8,11}
     
991. 778:n={0-38}+{1,1,2,3,5,6,8,11}
     
992. 779:n={0-38}+{1,1,2,2,3,4,6,8,11}
     
993. 780:n={0-38}+{}
     
994. 781:n={0-39}+{1}
     
995. 782:n={0-39}+{2}
     
996. 783:n={0-39}+{1,2}
     
997. 784:n={0-39}+{1,3}
     
998. 785:n={0-39}+{1,1,3}
     
999. 786:n={0-39}+{1,2,3}
     
1000. 787:n={0-39}+{1,2,4}
      
1001. 788:n={0-39}+{1,1,2,4}
      
1002. 789:n={0-39}+{1,1,3,4}
      
1003. 790:n={0-39}+{1,2,3,4}
      
1004. 791:n={0-39}+{1,2,3,5}
      
1005. 792:n={0-39}+{1,1,2,3,5}
      
1006. 793:n={0-39}+{1,1,2,3,6}
      
1007. 794:n={0-39}+{1,1,2,4,6}
      
1008. 795:n={0-39}+{1,2,3,4,5}
      
1009. 796:n={0-39}+{1,2,3,4,6}
      
1010. 797:n={0-39}+{1,1,2,3,4,6}
      
1011. 798:n={0-39}+{1,2,3,5,7}
      
1012. 799:n={0-39}+{1,1,2,3,5,7}
      
1013. 800:n={0-39}+{1,1,2,3,5,8}
      
1014. 801:n={0-39}+{1,1,2,4,5,8}
      
1015. 802:n={0-39}+{1,2,3,4,5,7}
      
1016. 803:n={0-39}+{1,2,3,4,5,8}
      
1017. 804:n={0-39}+{1,2,3,4,6,8}
      
1018. 805:n={0-39}+{1,1,2,3,4,6,8}
      
1019. 806:n={0-39}+{1,1,2,3,4,6,9}
      
1020. Prove by list failed for n=38
      
1021. Search for 38 elements
      
1022. 807:n={0-39}+{1,1,2,3,5,6,9}
      
1023. 808:n={0-39}+{1,1,2,3,5,7,9}
      
1024. 809:n={0-39}+{1,1,2,3,5,7,10}
      
1025. 810:n={0-39}+{1,2,3,4,5,6,9}
      
1026. 811:n={0-39}+{1,2,3,4,5,7,9}
      
1027. 812:n={0-39}+{1,1,2,3,4,5,7,9}
      
1028. 813:n={0-39}+{1,1,2,3,4,5,7,10}
      
1029. 814:n={0-39}+{1,1,2,3,4,6,7,10}
      
1030. 815:n={0-39}+{1,1,2,3,4,6,8,10}
      
1031. 816:n={0-39}+{1,1,2,3,4,6,8,11}
      
1032. 817:n={0-39}+{1,1,2,3,5,6,8,11}
      
1033. 818:n={0-39}+{1,1,2,2,3,4,6,8,11}
      
1034. Prove by list failed for n=38
      
1035. Search for 38 elements
      
1036. 819:n={0-39}+{1,2,3,4,5,6,8,10}
      
1037. 820:n={0-39}+{}
      
1038. 821:n={0-40}+{1}
      
1039. 822:n={0-40}+{2}
      
1040. 823:n={0-40}+{1,2}
      
1041. 824:n={0-40}+{1,3}
      
1042. 825:n={0-40}+{1,1,3}
      
1043. 826:n={0-40}+{1,2,3}
      
1044. 827:n={0-40}+{1,2,4}
      
1045. 828:n={0-40}+{1,1,2,4}
      
1046. 829:n={0-40}+{1,1,3,4}
      
1047. 830:n={0-40}+{1,2,3,4}
      
1048. 831:n={0-40}+{1,2,3,5}
      
1049. 832:n={0-40}+{1,1,2,3,5}
      
1050. 833:n={0-40}+{1,1,2,3,6}
      
1051. 834:n={0-40}+{1,1,2,4,6}
      
1052. 835:n={0-40}+{1,2,3,4,5}
      
1053. 836:n={0-40}+{1,2,3,4,6}
      
1054. 837:n={0-40}+{1,1,2,3,4,6}
      
1055. 838:n={0-40}+{1,1,2,3,4,7}
      
1056. 839:n={0-40}+{1,1,2,3,5,7}
      
1057. 840:n={0-40}+{1,1,2,3,5,8}
      
1058. 841:n={0-40}+{1,1,2,4,5,8}
      
1059. 842:n={0-40}+{1,2,3,4,5,7}
      
1060. 843:n={0-40}+{1,2,3,4,5,8}
      
1061. 844:n={0-40}+{1,2,3,4,6,8}
      
1062. 845:n={0-40}+{1,1,2,3,4,6,8}
      
1063. Prove by list failed for n=39
      
1064. Search for 39 elements
      
1065. 846:n={0-40}+{1,1,2,3,4,6,9}
      
1066. 847:n={0-40}+{1,1,2,3,5,6,9}
      
1067. 848:n={0-40}+{1,1,2,3,5,7,9}
      
1068. 849:n={0-40}+{1,1,2,3,5,7,10}
      
1069. 850:n={0-40}+{1,2,3,4,5,6,9}
      
1070. 851:n={0-40}+{1,2,3,4,5,7,9}
      
1071. 852:n={0-40}+{1,1,2,3,4,5,7,9}
      
1072. 853:n={0-40}+{1,1,2,3,4,5,7,10}
      
1073. 854:n={0-40}+{1,1,2,3,4,6,7,10}
      
1074. 855:n={0-40}+{1,1,2,3,4,6,8,10}
      
1075. 856:n={0-40}+{1,1,2,3,4,6,8,11}
      
1076. 857:n={0-40}+{1,1,2,3,5,6,8,11}
      
1077. Prove by list failed for n=39
      
1078. Search for 39 elements
      
1079. 858:n={0-40}+{1,1,2,2,3,4,6,8,11}
      
1080. 859:n={0-40}+{1,2,3,4,5,6,8,10}
      
1081. 860:n={0-40}+{1,2,3,4,5,6,8,11}
      
1082. 861:n={0-40}+{}
      
1083. 862:n={0-41}+{1}
      
1084. 863:n={0-41}+{2}
      
1085. 864:n={0-41}+{1,2}
      
1086. 865:n={0-41}+{1,3}
      
1087. 866:n={0-41}+{1,1,3}
      
1088. 867:n={0-41}+{1,2,3}
      
1089. 868:n={0-41}+{1,2,4}
      
1090. 869:n={0-41}+{1,1,2,4}
      
1091. 870:n={0-41}+{1,1,3,4}
      
1092. 871:n={0-41}+{1,2,3,4}
      
1093. 872:n={0-41}+{1,2,3,5}
      
1094. 873:n={0-41}+{1,1,2,3,5}
      
1095. 874:n={0-41}+{1,1,2,3,6}
      
1096. 875:n={0-41}+{1,1,2,4,6}
      
1097. 876:n={0-41}+{1,2,3,4,5}
      
1098. 877:n={0-41}+{1,2,3,4,6}
      
1099. 878:n={0-41}+{1,1,2,3,4,6}
      
1100. 879:n={0-41}+{1,1,2,3,4,7}
      
1101. 880:n={0-41}+{1,1,2,3,5,7}
      
1102. 881:n={0-41}+{1,1,2,3,5,8}
      
1103. 882:n={0-41}+{1,1,2,4,5,8}
      
1104. 883:n={0-41}+{1,2,3,4,5,7}
      
1105. 884:n={0-41}+{1,2,3,4,5,8}
      
1106. 885:n={0-41}+{1,2,3,4,6,8}
      
1107. Prove by list failed for n=40
      
1108. Search for 40 elements
      
1109. 886:n={0-41}+{1,1,2,3,4,6,8}
      
1110. 887:n={0-41}+{1,1,2,3,4,6,9}
      
1111. 888:n={0-41}+{1,1,2,3,5,6,9}
      
1112. 889:n={0-41}+{1,1,2,3,5,7,9}
      
1113. 890:n={0-41}+{1,1,2,3,5,7,10}
      
1114. 891:n={0-41}+{1,2,3,4,5,6,9}
      
1115. 892:n={0-41}+{1,2,3,4,5,7,9}
      
1116. 893:n={0-41}+{1,1,2,3,4,5,7,9}
      
1117. 894:n={0-41}+{1,1,2,3,4,5,7,10}
      
1118. 895:n={0-41}+{1,1,2,3,4,6,7,10}
      
1119. 896:n={0-41}+{1,1,2,3,4,6,8,10}
      
1120. 897:n={0-41}+{1,1,2,3,4,6,8,11}
      
1121. Prove by list failed for n=40
      
1122. Search for 40 elements
      
1123. 898:n={0-41}+{1,1,2,3,5,6,8,11}
      
1124. 899:n={0-41}+{1,1,2,2,3,4,6,8,11}
      
1125. 900:n={0-41}+{1,2,3,4,5,6,8,10}
      
1126. 901:n={0-41}+{1,2,3,4,5,6,8,11}
      
1127. 902:n={0-41}+{1,1,2,3,4,5,6,8,11}
      
1128. 903:n={0-41}+{}
      
1129. 904:n={0-42}+{1}
      
1130. 905:n={0-42}+{2}
      
1131. 906:n={0-42}+{1,2}
      
1132. 907:n={0-42}+{1,3}
      
1133. 908:n={0-42}+{1,1,3}
      
1134. 909:n={0-42}+{1,2,3}
      
1135. 910:n={0-42}+{1,2,4}
      
1136. 911:n={0-42}+{1,1,2,4}
      
1137. 912:n={0-42}+{1,1,3,4}
      
1138. 913:n={0-42}+{1,2,3,4}
      
1139. 914:n={0-42}+{1,2,3,5}
      
1140. 915:n={0-42}+{1,1,2,3,5}
      
1141. 916:n={0-42}+{1,1,2,3,6}
      
1142. 917:n={0-42}+{1,1,2,4,6}
      
1143. 918:n={0-42}+{1,2,3,4,5}
      
1144. 919:n={0-42}+{1,2,3,4,6}
      
1145. 920:n={0-42}+{1,1,2,3,4,6}
      
1146. 921:n={0-42}+{1,1,2,3,4,7}
      
1147. 922:n={0-42}+{1,1,2,3,5,7}
      
1148. 923:n={0-42}+{1,1,2,3,5,8}
      
1149. 924:n={0-42}+{1,1,2,4,5,8}
      
1150. 925:n={0-42}+{1,2,3,4,5,7}
      
1151. 926:n={0-42}+{1,2,3,4,5,8}
      
1152. Prove by list failed for n=41
      
1153. Search for 41 elements
      
1154. 927:n={0-42}+{1,2,3,4,6,8}
      
1155. 928:n={0-42}+{1,1,2,3,4,6,8}
      
1156. 929:n={0-42}+{1,1,2,3,4,6,9}
      
1157. 930:n={0-42}+{1,1,2,3,5,6,9}
      
1158. 931:n={0-42}+{1,1,2,3,5,7,9}
      
1159. 932:n={0-42}+{1,2,3,4,5,6,8}
      
1160. 933:n={0-42}+{1,2,3,4,5,6,9}
      
1161. 934:n={0-42}+{1,2,3,4,5,7,9}
      
1162. 935:n={0-42}+{1,1,2,3,4,5,7,9}
      
1163. 936:n={0-42}+{1,1,2,3,4,5,7,10}
      
1164. 937:n={0-42}+{1,1,2,3,4,6,7,10}
      
1165. 938:n={0-42}+{1,1,2,3,4,6,8,10}
      
1166. Prove by list failed for n=41
      
1167. Search for 41 elements
      
1168. 939:n={0-42}+{1,1,2,3,4,6,8,11}
      
1169. 940:n={0-42}+{1,1,2,3,5,6,8,11}
      
1170. 941:n={0-42}+{1,1,2,2,3,4,6,8,11}
      
1171. 942:n={0-42}+{1,2,3,4,5,6,8,10}
      
1172. 943:n={0-42}+{1,2,3,4,5,6,8,11}
      
1173. 944:n={0-42}+{1,1,2,3,4,5,6,8,11}
      
1174. 945:n={0-42}+{1,1,2,3,4,5,7,8,11}
      
1175. 946:n={0-42}+{}
      
1176. 947:n={0-43}+{1}
      
1177. 948:n={0-43}+{2}
      
1178. 949:n={0-43}+{1,2}
      
1179. 950:n={0-43}+{1,3}
      
1180. 951:n={0-43}+{1,1,3}
      
1181. 952:n={0-43}+{1,2,3}
      
1182. 953:n={0-43}+{1,2,4}
      
1183. 954:n={0-43}+{1,1,2,4}
      
1184. 955:n={0-43}+{1,1,3,4}
      
1185. 956:n={0-43}+{1,2,3,4}
      
1186. 957:n={0-43}+{1,2,3,5}
      
1187. 958:n={0-43}+{1,1,2,3,5}
      
1188. 959:n={0-43}+{1,1,2,3,6}
      
1189. 960:n={0-43}+{1,1,2,4,6}
      
1190. 961:n={0-43}+{1,2,3,4,5}
      
1191. 962:n={0-43}+{1,2,3,4,6}
      
1192. 963:n={0-43}+{1,1,2,3,4,6}
      
1193. 964:n={0-43}+{1,1,2,3,4,7}
      
1194. 965:n={0-43}+{1,1,2,3,5,7}
      
1195. 966:n={0-43}+{1,1,2,3,5,8}
      
1196. 967:n={0-43}+{1,1,2,4,5,8}
      
1197. 968:n={0-43}+{1,2,3,4,5,7}
      
1198. Prove by list failed for n=42
      
1199. Search for 42 elements
      
1200. 969:n={0-43}+{1,2,3,4,5,8}
      
1201. 970:n={0-43}+{1,2,3,4,6,8}
      
1202. 971:n={0-43}+{1,1,2,3,4,6,8}
      
1203. 972:n={0-43}+{1,1,2,3,4,6,9}
      
1204. 973:n={0-43}+{1,1,2,3,5,6,9}
      
1205. 974:n={0-43}+{1,1,2,3,5,7,9}
      
1206. 975:n={0-43}+{1,2,3,4,5,6,8}
      
1207. 976:n={0-43}+{1,2,3,4,5,6,9}
      
1208. 977:n={0-43}+{1,2,3,4,5,7,9}
      
1209. 978:n={0-43}+{1,1,2,3,4,5,7,9}
      
1210. 979:n={0-43}+{1,1,2,3,4,5,7,10}
      
1211. 980:n={0-43}+{1,1,2,3,4,6,7,10}
      
1212. Prove by list failed for n=42
      
1213. Search for 42 elements
      
1214. 981:n={0-43}+{1,1,2,3,4,6,8,10}
      
1215. 982:n={0-43}+{1,1,2,3,4,6,8,11}
      
1216. 983:n={0-43}+{1,1,2,3,5,6,8,11}
      
1217. 984:n={0-43}+{1,1,2,2,3,4,6,8,11}
      
1218. 985:n={0-43}+{1,2,3,4,5,6,8,10}
      
1219. 986:n={0-43}+{1,1,2,3,4,5,6,8,10}
      
1220. 987:n={0-43}+{1,1,2,3,4,5,6,8,11}
      
1221. 988:n={0-43}+{1,1,2,3,4,5,7,8,11}
      
1222. 989:n={0-43}+{1,1,2,3,4,5,7,9,11}
      
1223. 990:n={0-43}+{}
      
1224. 991:n={0-44}+{1}
      
1225. 992:n={0-44}+{2}
      
1226. 993:n={0-44}+{1,2}
      
1227. 994:n={0-44}+{1,3}
      
1228. 995:n={0-44}+{1,1,3}
      
1229. 996:n={0-44}+{1,2,3}
      
1230. 997:n={0-44}+{1,2,4}
      
1231. 998:n={0-44}+{1,1,2,4}
      
1232. 999:n={0-44}+{1,1,3,4}
      
1233. 1000:n={0-44}+{1,2,3,4}
      
1234. 1001:n={0-44}+{1,2,3,5}
      
1235. 1002:n={0-44}+{1,1,2,3,5}
      
1236. 1003:n={0-44}+{1,1,2,3,6}
      
1237. 1004:n={0-44}+{1,1,2,4,6}
      
1238. 1005:n={0-44}+{1,2,3,4,5}
      
1239. 1006:n={0-44}+{1,2,3,4,6}
      
1240. 1007:n={0-44}+{1,1,2,3,4,6}
      
1241. 1008:n={0-44}+{1,1,2,3,4,7}
      
1242. 1009:n={0-44}+{1,1,2,3,5,7}
      
1243. 1010:n={0-44}+{1,1,2,3,5,8}
      
1244. 1011:n={0-44}+{1,2,2,4,5,7}
      
1245. Prove by list failed for n=43
      
1246. Search for 43 elements
      
1247. 1012:n={0-44}+{1,2,3,4,5,7}
      
1248. 1013:n={0-44}+{1,2,3,4,5,8}
      
1249. 1014:n={0-44}+{1,2,3,4,6,8}
      
1250. 1015:n={0-44}+{1,1,2,3,4,6,8}
      
1251. 1016:n={0-44}+{1,1,2,3,4,6,9}
      
1252. 1017:n={0-44}+{1,1,2,3,5,6,9}
      
1253. 1018:n={0-44}+{1,1,2,3,5,7,9}
      
1254. 1019:n={0-44}+{1,2,3,4,5,6,8}
      
1255. 1020:n={0-44}+{1,2,3,4,5,6,9}
      
1256. 1021:n={0-44}+{1,2,3,4,5,7,9}
      
1257. 1022:n={0-44}+{1,1,2,3,4,5,7,9}
      
1258. 1023:n={0-44}+{1,1,2,3,4,5,7,10}
      
1259. Prove by list failed for n=43
      
1260. Search for 43 elements
      
1261. 1024:n={0-44}+{1,1,2,3,4,6,7,10}
      
1262. 1025:n={0-44}+{1,1,2,3,4,6,8,10}
      
1263. 1026:n={0-44}+{1,1,2,3,4,6,8,11}
      
1264. 1027:n={0-44}+{1,1,2,3,5,6,8,11}
      
1265. 1028:n={0-44}+{1,1,2,2,3,4,6,8,11}
      
1266. 1029:n={0-44}+{1,2,3,4,5,6,8,10}
      
1267. 1030:n={0-44}+{1,1,2,3,4,5,6,8,10}
      
1268. 1031:n={0-44}+{1,1,2,3,4,5,6,8,11}
      
1269. 1032:n={0-44}+{1,1,2,3,4,5,7,8,11}
      
1270. 1033:n={0-44}+{1,1,2,3,4,5,7,9,11}
      
1271. 1034:n={0-44}+{1,1,2,3,4,5,7,9,12}
      
1272. Prove by list failed for n=44
      
1273. Search for 44 elements
      
1274. 1035:n={0-44}+{}
      
1275. 1036:n={0-45}+{1}
      
1276. 1037:n={0-45}+{2}
      
1277. 1038:n={0-45}+{1,2}
      
1278. 1039:n={0-45}+{1,3}
      
1279. 1040:n={0-45}+{1,1,3}
      
1280. 1041:n={0-45}+{1,2,3}
      
1281. 1042:n={0-45}+{1,2,4}
      
1282. 1043:n={0-45}+{1,1,2,4}
      
1283. 1044:n={0-45}+{1,1,3,4}
      
1284. 1045:n={0-45}+{1,2,3,4}
      
1285. 1046:n={0-45}+{1,2,3,5}
      
1286. 1047:n={0-45}+{1,1,2,3,5}
      
1287. 1048:n={0-45}+{1,1,2,3,6}
      
1288. 1049:n={0-45}+{1,1,2,4,6}
      
1289. 1050:n={0-45}+{1,2,3,4,5}
      
1290. 1051:n={0-45}+{1,2,3,4,6}
      
1291. 1052:n={0-45}+{1,1,2,3,4,6}
      
1292. 1053:n={0-45}+{1,1,2,3,4,7}
      
1293. 1054:n={0-45}+{1,1,2,3,5,7}
      
1294. 1055:n={0-45}+{1,1,2,3,5,8}
      
1295. 1056:n={0-45}+{1,2,2,4,5,7}
      
1296. 1057:n={0-45}+{1,2,3,4,5,7}
      
1297. 1058:n={0-45}+{1,1,2,3,4,5,7}
      
1298. 1059:n={0-45}+{1,2,3,4,6,8}
      
1299. 1060:n={0-45}+{1,1,2,3,4,6,8}
      
1300. 1061:n={0-45}+{1,1,2,3,4,6,9}
      
1301. 1062:n={0-45}+{1,1,2,3,5,6,9}
      
1302. 1063:n={0-45}+{1,1,2,3,5,7,9}
      
1303. 1064:n={0-45}+{1,2,3,4,5,6,8}
      
1304. 1065:n={0-45}+{1,2,3,4,5,6,9}
      
1305. 1066:n={0-45}+{1,2,3,4,5,7,9}
      
1306. 1067:n={0-45}+{1,1,2,3,4,5,7,9}
      
1307. Prove by list failed for n=44
      
1308. Search for 44 elements
      
1309. 1068:n={0-45}+{1,1,2,3,4,5,7,10}
      
1310. 1069:n={0-45}+{1,1,2,3,4,6,7,10}
      
1311. 1070:n={0-45}+{1,1,2,3,4,6,8,10}
      
1312. 1071:n={0-45}+{1,1,2,3,4,6,8,11}
      
1313. 1072:n={0-45}+{1,1,2,3,5,6,8,11}
      
1314. 1073:n={0-45}+{1,1,2,2,3,4,6,8,11}
      
1315. 1074:n={0-45}+{1,2,3,4,5,6,8,10}
      
1316. 1075:n={0-45}+{1,1,2,3,4,5,6,8,10}
      
1317. 1076:n={0-45}+{1,1,2,3,4,5,6,8,11}
      
1318. 1077:n={0-45}+{1,1,2,3,4,5,7,8,11}
      
1319. 1078:n={0-45}+{1,1,2,3,4,5,7,9,11}
      
1320. 1079:n={0-45}+{1,1,2,3,4,5,7,9,12}
      
1321. 1080:n={0-45}+{1,1,2,3,4,6,7,9,12}
      
1322. 1081:n={0-45}+{}
      
1323. 1082:n={0-46}+{1}
      
1324. 1083:n={0-46}+{2}
      
1325. 1084:n={0-46}+{1,2}
      
1326. 1085:n={0-46}+{1,3}
      
1327. 1086:n={0-46}+{1,1,3}
      
1328. 1087:n={0-46}+{1,2,3}
      
1329. 1088:n={0-46}+{1,2,4}
      
1330. 1089:n={0-46}+{1,1,2,4}
      
1331. 1090:n={0-46}+{1,1,3,4}
      
1332. 1091:n={0-46}+{1,2,3,4}
      
1333. 1092:n={0-46}+{1,2,3,5}
      
1334. 1093:n={0-46}+{1,1,2,3,5}
      
1335. 1094:n={0-46}+{1,1,2,3,6}
      
1336. 1095:n={0-46}+{1,1,2,4,6}
      
1337. 1096:n={0-46}+{1,2,3,4,5}
      
1338. 1097:n={0-46}+{1,2,3,4,6}
      
1339. 1098:n={0-46}+{1,1,2,3,4,6}
      
1340. 1099:n={0-46}+{1,1,2,3,4,7}
      
1341. 1100:n={0-46}+{1,1,2,3,5,7}
      
1342. 1101:n={0-46}+{1,1,2,3,5,8}
      
1343. 1102:n={0-46}+{1,2,2,4,5,7}
      
1344. 1103:n={0-46}+{1,2,3,4,5,7}
      
1345. 1104:n={0-46}+{1,1,2,3,4,5,7}
      
1346. 1105:n={0-46}+{1,2,3,4,6,8}
      
1347. 1106:n={0-46}+{1,1,2,3,4,6,8}
      
1348. 1107:n={0-46}+{1,1,2,3,4,6,9}
      
1349. 1108:n={0-46}+{1,1,2,3,5,6,9}
      
1350. 1109:n={0-46}+{1,1,2,3,5,7,9}
      
1351. 1110:n={0-46}+{1,2,3,4,5,6,8}
      
1352. 1111:n={0-46}+{1,2,3,4,5,6,9}
      
1353. 1112:n={0-46}+{1,2,3,4,5,7,9}
      
1354. Prove by list failed for n=45
      
1355. Search for 45 elements
      
1356. 1113:n={0-46}+{1,1,2,3,4,5,7,9}
      
1357. 1114:n={0-46}+{1,1,2,3,4,5,7,10}
      
1358. 1115:n={0-46}+{1,1,2,3,4,6,7,10}
      
1359. 1116:n={0-46}+{1,1,2,3,4,6,8,10}
      
1360. 1117:n={0-46}+{1,1,2,3,4,6,8,11}
      
1361. 1118:n={0-46}+{1,2,2,3,4,6,8,11}
      
1362. 1119:n={0-46}+{1,1,2,2,3,4,6,8,11}
      
1363. 1120:n={0-46}+{1,2,3,4,5,6,8,10}
      
1364. 1121:n={0-46}+{1,1,2,3,4,5,6,8,10}
      
1365. 1122:n={0-46}+{1,1,2,3,4,5,6,8,11}
      
1366. 1123:n={0-46}+{1,1,2,3,4,5,7,8,11}
      
1367. 1124:n={0-46}+{1,1,2,3,4,5,7,9,11}
      
1368. 1125:n={0-46}+{1,1,2,3,4,5,7,9,12}
      
1369. Prove by list failed for n=45
      
1370. Search for 45 elements
      
1371. 1126:n={0-46}+{1,1,2,3,4,6,7,9,12}
      
1372. 1127:n={0-46}+{1,1,2,2,3,4,5,7,9,12}
      
1373. 1128:n={0-46}+{}
      
1374. 1129:n={0-47}+{1}
      
1375. 1130:n={0-47}+{2}
      
1376. 1131:n={0-47}+{1,2}
      
1377. 1132:n={0-47}+{1,3}
      
1378. 1133:n={0-47}+{1,1,3}
      
1379. 1134:n={0-47}+{1,2,3}
      
1380. 1135:n={0-47}+{1,2,4}
      
1381. 1136:n={0-47}+{1,1,2,4}
      
1382. 1137:n={0-47}+{1,1,3,4}
      
1383. 1138:n={0-47}+{1,2,3,4}
      
1384. 1139:n={0-47}+{1,2,3,5}
      
1385. 1140:n={0-47}+{1,1,2,3,5}
      
1386. 1141:n={0-47}+{1,1,2,3,6}
      
1387. 1142:n={0-47}+{1,1,2,4,6}
      
1388. 1143:n={0-47}+{1,2,3,4,5}
      
1389. 1144:n={0-47}+{1,2,3,4,6}
      
1390. 1145:n={0-47}+{1,1,2,3,4,6}
      
1391. 1146:n={0-47}+{1,1,2,3,4,7}
      
1392. 1147:n={0-47}+{1,1,2,3,5,7}
      
1393. 1148:n={0-47}+{1,1,2,3,5,8}
      
1394. 1149:n={0-47}+{1,2,2,4,5,7}
      
1395. 1150:n={0-47}+{1,2,3,4,5,7}
      
1396. 1151:n={0-47}+{1,1,2,3,4,5,7}
      
1397. 1152:n={0-47}+{1,1,2,3,4,5,8}
      
1398. 1153:n={0-47}+{1,1,2,3,4,6,8}
      
1399. 1154:n={0-47}+{1,1,2,3,4,6,9}
      
1400. 1155:n={0-47}+{1,1,2,3,5,6,9}
      
1401. 1156:n={0-47}+{1,1,2,3,5,7,9}
      
1402. 1157:n={0-47}+{1,2,3,4,5,6,8}
      
1403. 1158:n={0-47}+{1,2,3,4,5,6,9}
      
1404. Prove by list failed for n=46
      
1405. Search for 46 elements
      
1406. 1159:n={0-47}+{1,2,3,4,5,7,9}
      
1407. 1160:n={0-47}+{1,1,2,3,4,5,7,9}
      
1408. 1161:n={0-47}+{1,1,2,3,4,5,7,10}
      
1409. 1162:n={0-47}+{1,1,2,3,4,6,7,10}
      
1410. 1163:n={0-47}+{1,1,2,3,4,6,8,10}
      
1411. 1164:n={0-47}+{1,1,2,3,4,6,8,11}
      
1412. 1165:n={0-47}+{1,2,2,3,4,6,8,11}
      
1413. 1166:n={0-47}+{1,1,2,2,3,4,6,8,11}
      
1414. 1167:n={0-47}+{1,2,3,4,5,6,8,10}
      
1415. 1168:n={0-47}+{1,1,2,3,4,5,6,8,10}
      
1416. 1169:n={0-47}+{1,1,2,3,4,5,6,8,11}
      
1417. 1170:n={0-47}+{1,1,2,3,4,5,7,8,11}
      
1418. 1171:n={0-47}+{1,1,2,3,4,5,7,9,11}
      
1419. Prove by list failed for n=46
      
1420. Search for 46 elements
      
1421. 1172:n={0-47}+{1,1,2,3,4,5,7,9,12}
      
1422. 1173:n={0-47}+{1,1,2,3,4,6,7,9,12}
      
1423. 1174:n={0-47}+{1,1,2,2,3,4,5,7,9,12}
      
1424. 1175:n={0-47}+{1,1,2,2,3,4,6,7,9,12}
      
1425. 1176:n={0-47}+{}
      
1426. 1177:n={0-48}+{1}
      
1427. 1178:n={0-48}+{2}
      
1428. 1179:n={0-48}+{1,2}
      
1429. 1180:n={0-48}+{1,3}
      
1430. 1181:n={0-48}+{1,1,3}
      
1431. 1182:n={0-48}+{1,2,3}
      
1432. 1183:n={0-48}+{1,2,4}
      
1433. 1184:n={0-48}+{1,1,2,4}
      
1434. 1185:n={0-48}+{1,1,3,4}
      
1435. 1186:n={0-48}+{1,2,3,4}
      
1436. 1187:n={0-48}+{1,2,3,5}
      
1437. 1188:n={0-48}+{1,1,2,3,5}
      
1438. 1189:n={0-48}+{1,1,2,3,6}
      
1439. 1190:n={0-48}+{1,1,2,4,6}
      
1440. 1191:n={0-48}+{1,2,3,4,5}
      
1441. 1192:n={0-48}+{1,2,3,4,6}
      
1442. 1193:n={0-48}+{1,1,2,3,4,6}
      
1443. 1194:n={0-48}+{1,1,2,3,4,7}
      
1444. 1195:n={0-48}+{1,1,2,3,5,7}
      
1445. 1196:n={0-48}+{1,1,2,3,5,8}
      
1446. 1197:n={0-48}+{1,2,2,4,5,7}
      
1447. 1198:n={0-48}+{1,2,3,4,5,7}
      
1448. 1199:n={0-48}+{1,1,2,3,4,5,7}
      
1449. 1200:n={0-48}+{1,1,2,3,4,5,8}
      
1450. 1201:n={0-48}+{1,1,2,3,4,6,8}
      
1451. 1202:n={0-48}+{1,1,2,3,4,6,9}
      
1452. 1203:n={0-48}+{1,1,2,3,5,6,9}
      
1453. 1204:n={0-48}+{1,1,2,3,5,7,9}
      
1454. 1205:n={0-48}+{1,2,3,4,5,6,8}
      
1455. Prove by list failed for n=47
      
1456. Search for 47 elements
      
1457. 1206:n={0-48}+{1,2,3,4,5,6,9}
      
1458. 1207:n={0-48}+{1,2,3,4,5,7,9}
      
1459. 1208:n={0-48}+{1,1,2,3,4,5,7,9}
      
1460. 1209:n={0-48}+{1,1,2,3,4,5,7,10}
      
1461. 1210:n={0-48}+{1,1,2,3,4,6,7,10}
      
1462. 1211:n={0-48}+{1,1,2,3,4,6,8,10}
      
1463. 1212:n={0-48}+{1,1,2,3,4,6,8,11}
      
1464. 1213:n={0-48}+{1,2,2,3,4,6,8,11}
      
1465. 1214:n={0-48}+{1,1,2,2,3,4,6,8,11}
      
1466. 1215:n={0-48}+{1,2,3,4,5,6,8,10}
      
1467. 1216:n={0-48}+{1,1,2,3,4,5,6,8,10}
      
1468. 1217:n={0-48}+{1,1,2,3,4,5,6,8,11}
      
1469. 1218:n={0-48}+{1,1,2,3,4,5,7,8,11}
      
1470. Prove by list failed for n=47
      
1471. Search for 47 elements
      
1472. 1219:n={0-48}+{1,1,2,3,4,5,7,9,11}
      
1473. 1220:n={0-48}+{1,1,2,3,4,5,7,9,12}
      
1474. 1221:n={0-48}+{1,1,2,3,4,6,7,9,12}
      
1475. 1222:n={0-48}+{1,1,2,2,3,4,5,7,9,12}
      
1476. 1223:n={0-48}+{1,1,2,2,3,4,6,7,9,12}
      
1477. 1224:n={0-48}+{1,1,2,3,4,6,8,10,13}
      
1478. 1225:n={0-48}+{}
      
1479. 1226:n={0-49}+{1}
      
1480. 1227:n={0-49}+{2}
      
1481. 1228:n={0-49}+{1,2}
      
1482. 1229:n={0-49}+{1,3}
      
1483. 1230:n={0-49}+{1,1,3}
      
1484. 1231:n={0-49}+{1,2,3}
      
1485. 1232:n={0-49}+{1,2,4}
      
1486. 1233:n={0-49}+{1,1,2,4}
      
1487. 1234:n={0-49}+{1,1,3,4}
      
1488. 1235:n={0-49}+{1,2,3,4}
      
1489. 1236:n={0-49}+{1,2,3,5}
      
1490. 1237:n={0-49}+{1,1,2,3,5}
      
1491. 1238:n={0-49}+{1,1,2,3,6}
      
1492. 1239:n={0-49}+{1,1,2,4,6}
      
1493. 1240:n={0-49}+{1,2,3,4,5}
      
1494. 1241:n={0-49}+{1,2,3,4,6}
      
1495. 1242:n={0-49}+{1,1,2,3,4,6}
      
1496. 1243:n={0-49}+{1,1,2,3,4,7}
      
1497. 1244:n={0-49}+{1,1,2,3,5,7}
      
1498. 1245:n={0-49}+{1,1,2,3,5,8}
      
1499. 1246:n={0-49}+{1,2,2,4,5,7}
      
1500. 1247:n={0-49}+{1,2,3,4,5,7}
      
1501. 1248:n={0-49}+{1,1,2,3,4,5,7}
      
1502. 1249:n={0-49}+{1,1,2,3,4,5,8}
      
1503. 1250:n={0-49}+{1,1,2,3,4,6,8}
      
1504. 1251:n={0-49}+{1,1,2,3,4,6,9}
      
1505. 1252:n={0-49}+{1,1,2,3,5,6,9}
      
1506. 1253:n={0-49}+{1,1,2,3,5,7,9}
      
1507. Prove by list failed for n=48
      
1508. Search for 48 elements
      
1509. 1254:n={0-49}+{1,2,3,4,5,6,8}
      
1510. 1255:n={0-49}+{1,2,3,4,5,6,9}
      
1511. 1256:n={0-49}+{1,2,3,4,5,7,9}
      
1512. 1257:n={0-49}+{1,1,2,3,4,5,7,9}
      
1513. 1258:n={0-49}+{1,1,2,3,4,5,7,10}
      
1514. 1259:n={0-49}+{1,1,2,3,4,6,7,10}
      
1515. 1260:n={0-49}+{1,1,2,3,4,6,8,10}
      
1516. 1261:n={0-49}+{1,1,2,3,4,6,8,11}
      
1517. 1262:n={0-49}+{1,1,2,2,3,4,6,8,10}
      
1518. 1263:n={0-49}+{1,1,2,2,3,4,6,8,11}
      
1519. 1264:n={0-49}+{1,2,3,4,5,6,8,10}
      
1520. 1265:n={0-49}+{1,1,2,3,4,5,6,8,10}
      
1521. 1266:n={0-49}+{1,1,2,3,4,5,6,8,11}
      
1522. Prove by list failed for n=48
      
1523. Search for 48 elements
      
1524. 1267:n={0-49}+{1,1,2,3,4,5,7,8,11}
      
1525. 1268:n={0-49}+{1,1,2,3,4,5,7,9,11}
      
1526. 1269:n={0-49}+{1,1,2,3,4,5,7,9,12}
      
1527. 1270:n={0-49}+{1,1,2,3,4,6,7,9,12}
      
1528. 1271:n={0-49}+{1,1,2,2,3,4,5,7,9,12}
      
1529. 1272:n={0-49}+{1,1,2,2,3,4,6,7,9,12}
      
1530. 1273:n={0-49}+{1,1,2,2,3,4,6,7,9,13}
      
1531. 1274:n={0-49}+{1,1,2,3,4,5,6,7,9,11}
      
1532. 1275:n={0-49}+{}
      
1533. 1276:n={0-50}+{1}
      
1534. 1277:n={0-50}+{2}
      
1535. 1278:n={0-50}+{1,2}
      
1536. 1279:n={0-50}+{1,3}
      
1537. 1280:n={0-50}+{1,1,3}
      
1538. 1281:n={0-50}+{1,2,3}
      
1539. 1282:n={0-50}+{1,2,4}
      
1540. 1283:n={0-50}+{1,1,2,4}
      
1541. 1284:n={0-50}+{1,1,3,4}
      
1542. 1285:n={0-50}+{1,2,3,4}
      
1543. 1286:n={0-50}+{1,2,3,5}
      
1544. 1287:n={0-50}+{1,1,2,3,5}
      
1545. 1288:n={0-50}+{1,1,2,3,6}
      
1546. 1289:n={0-50}+{1,1,2,4,6}
      
1547. 1290:n={0-50}+{1,2,3,4,5}
      
1548. 1291:n={0-50}+{1,2,3,4,6}
      
1549. 1292:n={0-50}+{1,1,2,3,4,6}
      
1550. 1293:n={0-50}+{1,1,2,3,4,7}
      
1551. 1294:n={0-50}+{1,1,2,3,5,7}
      
1552. 1295:n={0-50}+{1,1,2,3,5,8}
      
1553. 1296:n={0-50}+{1,2,2,4,5,7}
      
1554. 1297:n={0-50}+{1,2,3,4,5,7}
      
1555. 1298:n={0-50}+{1,1,2,3,4,5,7}
      
1556. 1299:n={0-50}+{1,1,2,3,4,5,8}
      
1557. 1300:n={0-50}+{1,1,2,3,4,6,8}
      
1558. 1301:n={0-50}+{1,1,2,3,4,6,9}
      
1559. 1302:n={0-50}+{1,1,2,3,5,6,9}
      
1560. Prove by list failed for n=49
      
1561. Search for 49 elements
      
1562. 1303:n={0-50}+{1,1,2,3,5,7,9}
      
1563. 1304:n={0-50}+{1,2,3,4,5,6,8}
      
1564. 1305:n={0-50}+{1,2,3,4,5,6,9}
      
1565. 1306:n={0-50}+{1,2,3,4,5,7,9}
      
1566. 1307:n={0-50}+{1,1,2,3,4,5,7,9}
      
1567. 1308:n={0-50}+{1,1,2,3,4,5,7,10}
      
1568. 1309:n={0-50}+{1,1,2,3,4,6,7,10}
      
1569. 1310:n={0-50}+{1,1,2,3,4,6,8,10}
      
1570. 1311:n={0-50}+{1,1,2,3,4,6,8,11}
      
1571. 1312:n={0-50}+{1,1,2,2,3,4,6,8,10}
      
1572. 1313:n={0-50}+{1,1,2,2,3,4,6,8,11}
      
1573. 1314:n={0-50}+{1,2,3,4,5,6,8,10}
      
1574. 1315:n={0-50}+{1,1,2,3,4,5,6,8,10}
      
1575. Prove by list failed for n=49
      
1576. Search for 49 elements
      
1577. 1316:n={0-50}+{1,1,2,3,4,5,6,8,11}
      
1578. 1317:n={0-50}+{1,1,2,3,4,5,7,8,11}
      
1579. 1318:n={0-50}+{1,1,2,3,4,5,7,9,11}
      
1580. 1319:n={0-50}+{1,1,2,3,4,5,7,9,12}
      
1581. 1320:n={0-50}+{1,1,2,3,4,6,7,9,12}
      
1582. 1321:n={0-50}+{1,1,2,2,3,4,5,7,9,12}
      
1583. 1322:n={0-50}+{1,1,2,2,3,4,6,7,9,12}
      
1584. 1323:n={0-50}+{1,1,2,2,3,4,6,7,9,13}
      
1585. 1324:n={0-50}+{1,1,2,3,4,5,6,7,9,11}
      
1586. 1325:n={0-50}+{1,1,2,3,4,5,6,7,9,12}
      
1587. 1326:n={0-50}+{}
      
1588. 1327:n={0-51}+{1}
      
1589. 1328:n={0-51}+{2}
      
1590. 1329:n={0-51}+{1,2}
      
1591. 1330:n={0-51}+{1,3}
      
1592. 1331:n={0-51}+{1,1,3}
      
1593. 1332:n={0-51}+{1,2,3}
      
1594. 1333:n={0-51}+{1,2,4}
      
1595. 1334:n={0-51}+{1,1,2,4}
      
1596. 1335:n={0-51}+{1,1,3,4}
      
1597. 1336:n={0-51}+{1,2,3,4}
      
1598. 1337:n={0-51}+{1,2,3,5}
      
1599. 1338:n={0-51}+{1,1,2,3,5}
      
1600. 1339:n={0-51}+{1,1,2,3,6}
      
1601. 1340:n={0-51}+{1,1,2,4,6}
      
1602. 1341:n={0-51}+{1,2,3,4,5}
      
1603. 1342:n={0-51}+{1,2,3,4,6}
      
1604. 1343:n={0-51}+{1,1,2,3,4,6}
      
1605. 1344:n={0-51}+{1,1,2,3,4,7}
      
1606. 1345:n={0-51}+{1,1,2,3,5,7}
      
1607. 1346:n={0-51}+{1,1,2,3,5,8}
      
1608. 1347:n={0-51}+{1,2,2,4,5,7}
      
1609. 1348:n={0-51}+{1,2,3,4,5,7}
      
1610. 1349:n={0-51}+{1,1,2,3,4,5,7}
      
1611. 1350:n={0-51}+{1,1,2,3,4,5,8}
      
1612. 1351:n={0-51}+{1,1,2,3,4,6,8}
      
1613. 1352:n={0-51}+{1,1,2,3,4,6,9}
      
1614. 1353:n={0-51}+{1,1,2,3,5,6,9}
      
1615. 1354:n={0-51}+{1,1,2,3,5,7,9}
      
1616. 1355:n={0-51}+{1,2,3,4,5,6,8}
      
1617. 1356:n={0-51}+{1,2,3,4,5,6,9}
      
1618. 1357:n={0-51}+{1,2,3,4,5,7,9}
      
1619. 1358:n={0-51}+{1,1,2,3,4,5,7,9}
      
1620. 1359:n={0-51}+{1,1,2,3,4,5,7,10}
      
1621. 1360:n={0-51}+{1,1,2,3,4,6,7,10}
      
1622. 1361:n={0-51}+{1,1,2,3,4,6,8,10}
      
1623. 1362:n={0-51}+{1,1,2,3,4,6,8,11}
      
1624. 1363:n={0-51}+{1,1,2,2,3,4,6,8,10}
      
1625. 1364:n={0-51}+{1,1,2,2,3,4,6,8,11}
      
1626. 1365:n={0-51}+{1,2,3,4,5,6,8,10}
      
1627. Prove by list failed for n=50
      
1628. Search for 50 elements
      
1629. 1366:n={0-51}+{1,1,2,3,4,5,6,8,10}
      
1630. 1367:n={0-51}+{1,1,2,3,4,5,6,8,11}
      
1631. 1368:n={0-51}+{1,1,2,3,4,5,7,8,11}
      
1632. 1369:n={0-51}+{1,1,2,3,4,5,7,9,11}
      
1633. 1370:n={0-51}+{1,1,2,3,4,5,7,9,12}
      
1634. 1371:n={0-51}+{1,1,2,3,4,6,7,9,12}
      
1635. 1372:n={0-51}+{1,1,2,2,3,4,5,7,9,12}
      
1636. 1373:n={0-51}+{1,1,2,2,3,4,6,7,9,12}
      
1637. 1374:n={0-51}+{1,1,2,2,3,4,6,7,9,13}
      
1638. 1375:n={0-51}+{1,1,2,3,4,5,6,7,9,11}
      
1639. 1376:n={0-51}+{1,1,2,3,4,5,6,7,9,12}
      
1640. 1377:n={0-51}+{1,1,2,3,4,5,6,8,9,12}
      
1641. 1378:n={0-51}+{}
      
1642. 1379:n={0-52}+{1}
      
1643. 1380:n={0-52}+{2}
      
1644. 1381:n={0-52}+{1,2}
      
1645. 1382:n={0-52}+{1,3}
      
1646. 1383:n={0-52}+{1,1,3}
      
1647. 1384:n={0-52}+{1,2,3}
      
1648. 1385:n={0-52}+{1,2,4}
      
1649. 1386:n={0-52}+{1,1,2,4}
      
1650. 1387:n={0-52}+{1,1,3,4}
      
1651. 1388:n={0-52}+{1,2,3,4}
      
1652. 1389:n={0-52}+{1,2,3,5}
      
1653. 1390:n={0-52}+{1,1,2,3,5}
      
1654. 1391:n={0-52}+{1,1,2,3,6}
      
1655. 1392:n={0-52}+{1,1,2,4,6}
      
1656. 1393:n={0-52}+{1,2,3,4,5}
      
1657. 1394:n={0-52}+{1,2,3,4,6}
      
1658. 1395:n={0-52}+{1,1,2,3,4,6}
      
1659. 1396:n={0-52}+{1,1,2,3,4,7}
      
1660. 1397:n={0-52}+{1,1,2,3,5,7}
      
1661. 1398:n={0-52}+{1,1,2,3,5,8}
      
1662. 1399:n={0-52}+{1,2,2,4,5,7}
      
1663. 1400:n={0-52}+{1,2,3,4,5,7}
      
1664. 1401:n={0-52}+{1,1,2,3,4,5,7}
      
1665. 1402:n={0-52}+{1,1,2,3,4,5,8}
      
1666. 1403:n={0-52}+{1,1,2,3,4,6,8}
      
1667. 1404:n={0-52}+{1,1,2,3,4,6,9}
      
1668. 1405:n={0-52}+{1,1,2,3,5,6,9}
      
1669. 1406:n={0-52}+{1,1,2,3,5,7,9}
      
1670. 1407:n={0-52}+{1,2,3,4,5,6,8}
      
1671. 1408:n={0-52}+{1,2,3,4,5,6,9}
      
1672. 1409:n={0-52}+{1,2,3,4,5,7,9}
      
1673. 1410:n={0-52}+{1,1,2,3,4,5,7,9}
      
1674. 1411:n={0-52}+{1,1,2,3,4,5,7,10}
      
1675. 1412:n={0-52}+{1,1,2,3,4,6,7,10}
      
1676. 1413:n={0-52}+{1,1,2,3,4,6,8,10}
      
1677. 1414:n={0-52}+{1,1,2,3,4,6,8,11}
      
1678. 1415:n={0-52}+{1,1,2,2,3,4,6,8,10}
      
1679. 1416:n={0-52}+{1,1,2,2,3,4,6,8,11}
      
1680. Prove by list failed for n=51
      
1681. Search for 51 elements
      
1682. 1417:n={0-52}+{1,2,3,4,5,6,8,10}
      
1683. 1418:n={0-52}+{1,1,2,3,4,5,6,8,10}
      
1684. 1419:n={0-52}+{1,1,2,3,4,5,6,8,11}
      
1685. 1420:n={0-52}+{1,1,2,3,4,5,7,8,11}
      
1686. 1421:n={0-52}+{1,1,2,3,4,5,7,9,11}
      
1687. 1422:n={0-52}+{1,1,2,3,4,5,7,9,12}
      
1688. 1423:n={0-52}+{1,1,2,3,4,6,7,9,12}
      
1689. 1424:n={0-52}+{1,1,2,2,3,4,5,7,9,12}
      
1690. 1425:n={0-52}+{1,1,2,2,3,4,6,7,9,12}
      
1691. 1426:n={0-52}+{1,1,2,2,3,4,6,7,9,13}
      
1692. 1427:n={0-52}+{1,1,2,3,4,5,6,7,9,11}
      
1693. 1428:n={0-52}+{1,1,2,3,4,5,6,7,9,12}
      
1694. 1429:n={0-52}+{1,1,2,3,4,5,6,8,9,12}
      
1695. 1430:n={0-52}+{1,1,2,3,4,5,6,8,10,12}
      
1696. 1431:n={0-52}+{}
      
1697. 1432:n={0-53}+{1}
      
1698. 1433:n={0-53}+{2}
      
1699. 1434:n={0-53}+{1,2}
      
1700. 1435:n={0-53}+{1,3}
      
1701. 1436:n={0-53}+{1,1,3}
      
1702. 1437:n={0-53}+{1,2,3}
      
1703. 1438:n={0-53}+{1,2,4}
      
1704. 1439:n={0-53}+{1,1,2,4}
      
1705. 1440:n={0-53}+{1,1,3,4}
      
1706. 1441:n={0-53}+{1,2,3,4}
      
1707. 1442:n={0-53}+{1,2,3,5}
      
1708. 1443:n={0-53}+{1,1,2,3,5}
      
1709. 1444:n={0-53}+{1,1,2,3,6}
      
1710. 1445:n={0-53}+{1,1,2,4,6}
      
1711. 1446:n={0-53}+{1,2,3,4,5}
      
1712. 1447:n={0-53}+{1,2,3,4,6}
      
1713. 1448:n={0-53}+{1,1,2,3,4,6}
      
1714. 1449:n={0-53}+{1,1,2,3,4,7}
      
1715. 1450:n={0-53}+{1,1,2,3,5,7}
      
1716. 1451:n={0-53}+{1,1,2,3,5,8}
      
1717. 1452:n={0-53}+{1,2,2,4,5,7}
      
1718. 1453:n={0-53}+{1,2,3,4,5,7}
      
1719. 1454:n={0-53}+{1,1,2,3,4,5,7}
      
1720. 1455:n={0-53}+{1,1,2,3,4,5,8}
      
1721. 1456:n={0-53}+{1,1,2,3,4,6,8}
      
1722. 1457:n={0-53}+{1,1,2,3,4,6,9}
      
1723. 1458:n={0-53}+{1,1,2,3,5,6,9}
      
1724. 1459:n={0-53}+{1,1,2,3,5,7,9}
      
1725. 1460:n={0-53}+{1,2,3,4,5,6,8}
      
1726. 1461:n={0-53}+{1,1,2,3,4,5,6,8}
      
1727. 1462:n={0-53}+{1,2,3,4,5,7,9}
      
1728. 1463:n={0-53}+{1,1,2,3,4,5,7,9}
      
1729. 1464:n={0-53}+{1,1,2,3,4,5,7,10}
      
1730. 1465:n={0-53}+{1,1,2,3,4,6,7,10}
      
1731. 1466:n={0-53}+{1,1,2,3,4,6,8,10}
      
1732. 1467:n={0-53}+{1,1,2,3,4,6,8,11}
      
1733. 1468:n={0-53}+{1,1,2,2,3,4,6,8,10}
      
1734. Prove by list failed for n=52
      
1735. Search for 52 elements
      
1736. 1469:n={0-53}+{1,1,2,2,3,4,6,8,11}
      
1737. 1470:n={0-53}+{1,2,3,4,5,6,8,10}
      
1738. 1471:n={0-53}+{1,1,2,3,4,5,6,8,10}
      
1739. 1472:n={0-53}+{1,1,2,3,4,5,6,8,11}
      
1740. 1473:n={0-53}+{1,1,2,3,4,5,7,8,11}
      
1741. 1474:n={0-53}+{1,1,2,3,4,5,7,9,11}
      
1742. 1475:n={0-53}+{1,1,2,3,4,5,7,9,12}
      
1743. 1476:n={0-53}+{1,2,2,3,4,5,7,9,12}
      
1744. 1477:n={0-53}+{1,1,2,2,3,4,5,7,9,12}
      
1745. 1478:n={0-53}+{1,1,2,2,3,4,6,7,9,12}
      
1746. 1479:n={0-53}+{1,1,2,2,3,4,6,7,9,13}
      
1747. 1480:n={0-53}+{1,1,2,3,4,5,6,7,9,11}
      
1748. 1481:n={0-53}+{1,1,2,3,4,5,6,7,9,12}
      
1749. 1482:n={0-53}+{1,1,2,3,4,5,6,8,9,12}
      

复制代码

王守恩

mathe 发表于 2025-3-23 22:06
修正bug并且在验证失败时继续搜索，非常明显，遇到验证失败后，继续搜索会非常慢；如果没有遇到验证失败， ...

大胆的往前走！
2——2——0,
5——3——1,
9——4——2——3,
14——5——2——1,3,
20——6——3,
27——7——4——2,4,
35——8——4——1,2,4,
44——9——5,
54——10——6,
65——11——7——1,3,6,
77——12——7——1,2,3,5,
90——13——8,
104——14——9,
119——15——10——1,2,4,7,
135——16——10——1,1,2,4,7,
152——17——11,
170——18——12,
189——19——13,
209——20——14——1,2,3,5,8,
230——21——14——1,1,2,3,5,8,
252——22——15,
275——23——16,
299——24——17,
324——25——18,
350——26——19——1,2,3,4,6,9,
377——27——19——1,1,2,3,4,6,9,
405——28——20,
434——29——21,
464——30——22,
495——31——23,  
527——32——24,  
560——33——25——1,2,3,4,5,7,10,
594——34——25——1,1,2,3,4,5,7,10,  
629——35——26,
665——36——27,
702——37——28,
740——38——29,
779——39——30,
819——40——31,
860——41——32——1,2,3,4,5,6,8,11,
902——42——32——1,1,1,3,4,5,6,8,11,
945——43——33,
989——44——34,
1034——45——35,
1080——46——36,
1127——47——37,
1175——48——38,
1224——49——39,
1274——50——40——1,2,3,4,5,6,7,9,12,
1325——51——40——1,1,2,3,4,5,6,7,9,12,
1377——52——41,
1430——53——42,
1484——54——43,
1539——55——44,
1595——56——45,
1652——57——46,
1710——58——47,
1769——59——48,
1829——60——49——1,2,3,4,5,6,7,8,10,13,
1890——61——49——1,1,2,3,4,5,6,7,8,10,13,
1952——62——50,
2015——63——51,
2079——64——52,
2144——65——53,
2210——66——54,
2277——67——55,
2345——68——56,
2414——69——57,
2484——70——58,
2555——71——59——1,2,3,4,5,6,7,8,9,11,14,
2627——72——59——1,1,2,3,4,5,6,7,8,9,11,14,
2700——73——60,
2774——74——61,
2849——75——62,
2925——76——63,
3002——77——64,
说明。譬如
2015——63——51
2015: 共63个数, 2015是使用0-51连续数的最后一个。