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。
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
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。
我给出Mathematica的代码。100的结果是
{13,{1,2,3,4,5,6,7,8,9,10,12,15,18}}
Block[{s = 100, n, exp}, n = Floor)];
product = 0; ans = {};
Do;
exp = Total == s && Less @@ Flatten[{0, params, s}];
Do . {1, -1}];
If, {p, SolveValues}], {i, n}]; ans]
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！
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
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
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。
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。
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
#include <gmpxx.h>
#include <math.h>
#include <algorithm>
#include <iostream>
#ifndef UB
#define UB 2025
#endif
int SUM;
mpz_class curbest;
int blist;
int bdepth;
int bsn;
int depth;
int maxn;
int leftv;
int searchn;
int tc;
int ilist;
int clist;//max depth must be smaller than SUM
//
void initmaxn()
{
int h;
leftv=0;
for(h=1;;h++){
if(h*(h+1)/2>SUM){
maxn=h-1;
leftv=SUM-maxn*(maxn+1)/2;
return;
}
}
}
void check_last()
{
int i,j;
for(i=0;i<searchn;i++){
ilist=i+1;
}
for(i=0;i<depth;i++){
ilist+=clist;
}
mpz_class v=1;
for(i=0;i<searchn;i++){
v*=ilist;
for(j=i+1;j<searchn;j++){
v*=ilist-ilist;
}
}
tc++;
if(v>curbest){
curbest=v;
bdepth=depth;
#ifdef DUMP
std::cout<<"Found "<<tc<<" {";
#endif
for(i=0;i<depth;i++){
blist=clist;
#ifdef DUMP
std::cout<<' '<<clist;
#endif
}
bsn=searchn;
#ifdef DUMP
std::cout<<"}: "<<curbest<<std::endl;
#endif
}
}
void search()
{
int i;
int send;
send=leftv;
if(leftv==0){
check_last();
return;
}
if(depth>0&&send>clist)send=clist;
for(i=1;i<=send;i++){
clist=i;
leftv-=i;
depth++;
if(depth<=searchn){
search();
}
depth--;
leftv+=i;
}
}
mpq_class mpqpower(const mpq_class& x, int b)
{
mpq_class p=1,m=x;
while(b){
if(b&1)p*=m;
m*=m;
b>>=1;
}
return p;
}
mpz_class intpower(int a, int b)
{
mpz_class p=1,m=a;
while(b){
if(b&1)p*=m;
m*=m;
b>>=1;
}
return p;
}
struct WeightValue{
int w;
mpq_class v;
};
void dumpWV(WeightValue *values, int c)
{
int i;
for(i=0;i<c;i++){
std::cout<<values.w<<':'<<values.v<<std::endl;
}
}
void mergeSets(WeightValue *values, int& count)
{
int i,j;
bool increasing=false;
while(!increasing&&count>1){
increasing =true;
for(i=0,j=0;i<count-1;i++){
if(values.v*values.w>=values.v*values.w){//merge j and i+1
values.v+=values.v;
values.w+=values.w;
increasing = false;
}else{
if(j!=i){//moves i+1 to j+1
values.w=values.w;
values.v=values.v;
}
j++;
}
}
count=j+1;
}
#ifdef DUMP
std::cout<<"Value after merge:\n";
dumpWV(values,count);
#endif
}
bool prove(int n)
{
int i,s;
mpq_class *onlyv=new mpq_class;
WeightValue *values=new WeightValue;
s=0;
for(i=0;i<n;i++){
clist=i+1;
s+=i+1;
}
int psum=SUM-s;
while(psum>0){
int c=(int)(sqrt(1+8*psum)+1E-10);
c=(c-1)/2;
if((c*(c+1))/2>psum)c--;
for(i=0;i<c;i++){
clist+=c-i;
}
psum-=(c*(c+1))/2;
}
#ifdef DUMP
std::cout<<"Try to prove "<<n<<" using list {";
for(i=0;i<n;i++){
std::cout<<" "<<clist;
}
std::cout<<" }\n";
#endif
for(i=0;i<n;i++){
mpq_class t(1,clist);
values.w=1;
values.v+=t;
for(s=0;s<i;s++){
mpq_class t(1,clist-clist);
values.v+=t;
}
for(s=i+1;s<n;s++){
mpq_class t(1,clist-clist);
values.v-=t;
}
onlyv=values.v;
}
#ifdef DUMP
std::cout<<"values=[";
for(i=0;i<n;i++){
std::cout<<" "<<values.v;
}
std::cout<<" ]\n";
#endif
int nv=n;
mergeSets(values,nv);
#ifdef DUMP
std::cout<<"We need maximize value at index "<<n-values.w+1<<std::endl;
#endif
mpq_class fv=0;
for(i=0;i<n-values.w;i++){
fv+=onlyv*(i+1);
}
mpq_class extra(SUM-n*(n+1)/2, values.w);
for(i=n-values.w;i<n;i++){
fv+=onlyv*(i+1+extra);
}
delete []values;
delete []onlyv;
fv/=n*(n+1)/2;
fv=mpqpower(fv,n*(n+1)/2);
mpz_class iv=1;
for(i=0;i<n;i++){
iv*=clist;
for(s=i+1;s<n;s++){
iv*=clist-clist;
}
}
if(fv*iv<=curbest){
#ifdef DUMP
std::cout<<"Prove by list passed\n";
#endif
return true;
}else{
std::cout<<"Prove by list failed for n="<<n<<"\n";
return false;
}
}
void check_u(int n)
{
int i;
mpz_class num=1, den=1;
for(i=1;i<=n;i++){
den*=intpower(i,i);
}
for(i=1;i<=n;i++){
int v=SUM-(n-i+1)*(n-i)/2-i*(i-1)/2;
num*=intpower(v,n-i+1);
}
if(num<=curbest*den){
#ifdef DUMP
std::cout<<"U["<<SUM<<","<<n<<"] is less than best value\n";
#endif
}else{
#ifdef DUMP
std::cout<<"U["<<SUM<<","<<n<<"] is more than best value, more proving required\n";
#endif
if(!prove(n)){
searchn=n;
leftv=SUM - n*(n+1)/2;
std::cout<<"Search for "<<n<<" elements\n";
search();
}
}
}
int main()
{
int n;
for(SUM=3;SUM<=UB;SUM++){
initmaxn();
searchn=maxn;
#ifdef DUMP
std::cout<<"Max N = "<<maxn<<std::endl;
#endif
search();
#ifdef DUMP
std::cout<<"Total "<<tc<<" enumerated"<<std::endl;
#endif
for(n=maxn-1;n>=1;n--){
check_u(n);
}
std::cout<<SUM<<":n={0-"<<bsn<<"}+{";
int j;
for(j=bdepth-1;j>=0;j--){
if(j<bdepth-1)std::cout<<",";
std::cout<<blist;
}
std::cout<<"}\n";
fflush(stdout);
}
return 0;
}
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)
Prove by list failed for n=1
Search for 1 elements
3:n={0-1}+{2}
4:n={0-2}+{1}
5:n={0-2}+{2}
Prove by list failed for n=2
Search for 2 elements
6:n={0-2}+{3}
7:n={0-3}+{1}
8:n={0-3}+{2}
9:n={0-3}+{1,2}
Prove by list failed for n=3
Search for 3 elements
10:n={0-3}+{1,3}
11:n={0-4}+{1}
Prove by list failed for n=3
Search for 3 elements
12:n={0-4}+{2}
13:n={0-4}+{1,2}
14:n={0-4}+{1,3}
Prove by list failed for n=4
Search for 4 elements
15:n={0-4}+{1,4}
Prove by list failed for n=4
Search for 4 elements
16:n={0-5}+{1}
17:n={0-5}+{2}
18:n={0-5}+{1,2}
19:n={0-5}+{1,3}
Prove by list failed for n=4
Search for 4 elements
20:n={0-5}+{1,4}
Prove by list failed for n=5
Search for 5 elements
21:n={0-5}+{2,4}
Prove by list failed for n=5
Search for 5 elements
22:n={0-6}+{1}
23:n={0-6}+{2}
24:n={0-6}+{1,2}
Prove by list failed for n=5
Search for 5 elements
25:n={0-6}+{1,3}
26:n={0-6}+{1,4}
27:n={0-6}+{2,4}
Prove by list failed for n=6
Search for 6 elements
28:n={0-6}+{1,2,4}
29:n={0-7}+{1}
30:n={0-7}+{2}
Prove by list failed for n=6
Search for 6 elements
31:n={0-7}+{1,2}
32:n={0-7}+{1,3}
33:n={0-7}+{1,4}
34:n={0-7}+{2,4}
35:n={0-7}+{1,2,4}
Prove by list failed for n=7
Search for 7 elements
Prove by list failed for n=6
Search for 6 elements
36:n={0-7}+{1,2,5}
37:n={0-8}+{1}
Prove by list failed for n=7
Search for 7 elements
38:n={0-8}+{2}
39:n={0-8}+{1,2}
40:n={0-8}+{1,3}
41:n={0-8}+{1,4}
42:n={0-8}+{1,2,3}
Prove by list failed for n=7
Search for 7 elements
43:n={0-8}+{1,2,4}
44:n={0-8}+{1,2,5}
Prove by list failed for n=8
Search for 8 elements
45:n={0-8}+{}
Prove by list failed for n=8
Search for 8 elements
46:n={0-9}+{1}
47:n={0-9}+{2}
48:n={0-9}+{1,2}
49:n={0-9}+{1,3}
50:n={0-9}+{1,4}
Prove by list failed for n=8
Search for 8 elements
51:n={0-9}+{1,2,3}
52:n={0-9}+{1,2,4}
53:n={0-9}+{1,2,5}
54:n={0-9}+{1,3,5}
Prove by list failed for n=9
Search for 9 elements
55:n={0-9}+{}
56:n={0-10}+{1}
Prove by list failed for n=8
Search for 8 elements
57:n={0-10}+{2}
58:n={0-10}+{1,2}
59:n={0-10}+{1,3}
Prove by list failed for n=9
Search for 9 elements
60:n={0-10}+{1,4}
61:n={0-10}+{1,2,3}
62:n={0-10}+{1,2,4}
63:n={0-10}+{1,2,5}
64:n={0-10}+{1,3,5}
65:n={0-10}+{1,3,6}
Prove by list failed for n=10
Search for 10 elements
Prove by list failed for n=9
Search for 9 elements
66:n={0-10}+{}
67:n={0-11}+{1}
68:n={0-11}+{2}
69:n={0-11}+{1,2}
Prove by list failed for n=10
Search for 10 elements
70:n={0-11}+{1,3}
71:n={0-11}+{1,1,3}
72:n={0-11}+{1,2,3}
73:n={0-11}+{1,2,4}
74:n={0-11}+{1,2,5}
75:n={0-11}+{1,3,5}
Prove by list failed for n=10
Search for 10 elements
76:n={0-11}+{1,3,6}
77:n={0-11}+{1,2,3,5}
Prove by list failed for n=11
Search for 11 elements
78:n={0-11}+{}
79:n={0-12}+{1}
80:n={0-12}+{2}
Prove by list failed for n=11
Search for 11 elements
81:n={0-12}+{1,2}
82:n={0-12}+{1,3}
83:n={0-12}+{1,1,3}
84:n={0-12}+{1,2,3}
85:n={0-12}+{1,2,4}
86:n={0-12}+{1,2,5}
Prove by list failed for n=11
Search for 11 elements
87:n={0-12}+{1,3,5}
88:n={0-12}+{1,1,3,5}
89:n={0-12}+{1,2,3,5}
90:n={0-12}+{1,2,3,6}
91:n={0-12}+{}
92:n={0-13}+{1}
Prove by list failed for n=12
Search for 12 elements
93:n={0-13}+{2}
94:n={0-13}+{1,2}
95:n={0-13}+{1,3}
96:n={0-13}+{1,1,3}
97:n={0-13}+{1,2,3}
98:n={0-13}+{1,2,4}
Prove by list failed for n=12
Search for 12 elements
99:n={0-13}+{1,2,5}
100:n={0-13}+{1,3,5}
101:n={0-13}+{1,1,3,5}
102:n={0-13}+{1,2,3,5}
103:n={0-13}+{1,2,3,6}
104:n={0-13}+{1,2,4,6}
Prove by list failed for n=13
Search for 13 elements
105:n={0-13}+{}
Prove by list failed for n=13
Search for 13 elements
Prove by list failed for n=12
Search for 12 elements
106:n={0-14}+{1}
107:n={0-14}+{2}
108:n={0-14}+{1,2}
109:n={0-14}+{1,3}
110:n={0-14}+{1,1,3}
111:n={0-14}+{1,2,3}
Prove by list failed for n=13
Search for 13 elements
112:n={0-14}+{1,2,4}
113:n={0-14}+{1,2,5}
114:n={0-14}+{1,3,5}
115:n={0-14}+{1,1,3,5}
116:n={0-14}+{1,2,3,5}
117:n={0-14}+{1,2,3,6}
118:n={0-14}+{1,2,4,6}
Prove by list failed for n=13
Search for 13 elements
119:n={0-14}+{1,2,4,7}
Prove by list failed for n=14
Search for 14 elements
120:n={0-14}+{}
121:n={0-15}+{1}
122:n={0-15}+{2}
123:n={0-15}+{1,2}
124:n={0-15}+{1,3}
125:n={0-15}+{1,1,3}
Prove by list failed for n=14
Search for 14 elements
126:n={0-15}+{1,2,3}
127:n={0-15}+{1,2,4}
128:n={0-15}+{1,2,5}
129:n={0-15}+{1,3,5}
130:n={0-15}+{1,2,3,4}
131:n={0-15}+{1,2,3,5}
132:n={0-15}+{1,2,3,6}
Prove by list failed for n=14
Search for 14 elements
133:n={0-15}+{1,2,4,6}
134:n={0-15}+{1,2,4,7}
135:n={0-15}+{1,1,2,4,7}
136:n={0-15}+{}
137:n={0-16}+{1}
138:n={0-16}+{2}
139:n={0-16}+{1,2}
140:n={0-16}+{1,3}
Prove by list failed for n=15
Search for 15 elements
141:n={0-16}+{1,1,3}
142:n={0-16}+{1,2,3}
143:n={0-16}+{1,2,4}
144:n={0-16}+{1,2,5}
145:n={0-16}+{1,3,5}
146:n={0-16}+{1,2,3,4}
147:n={0-16}+{1,2,3,5}
Prove by list failed for n=15
Search for 15 elements
148:n={0-16}+{1,2,3,6}
149:n={0-16}+{1,2,4,6}
150:n={0-16}+{1,2,4,7}
151:n={0-16}+{1,1,2,4,7}
152:n={0-16}+{1,2,3,4,6}
153:n={0-16}+{}
154:n={0-17}+{1}
155:n={0-17}+{2}
156:n={0-17}+{1,2}
Prove by list failed for n=16
Search for 16 elements
157:n={0-17}+{1,3}
158:n={0-17}+{1,1,3}
159:n={0-17}+{1,2,3}
160:n={0-17}+{1,2,4}
161:n={0-17}+{1,2,5}
162:n={0-17}+{1,3,5}
163:n={0-17}+{1,2,3,4}
Prove by list failed for n=16
Search for 16 elements
164:n={0-17}+{1,2,3,5}
165:n={0-17}+{1,2,3,6}
166:n={0-17}+{1,2,4,6}
167:n={0-17}+{1,2,4,7}
168:n={0-17}+{1,1,2,4,7}
169:n={0-17}+{1,2,3,4,6}
170:n={0-17}+{1,2,3,4,7}
171:n={0-17}+{}
Prove by list failed for n=16
Search for 16 elements
172:n={0-18}+{1}
173:n={0-18}+{2}
Prove by list failed for n=17
Search for 17 elements
174:n={0-18}+{1,2}
175:n={0-18}+{1,3}
176:n={0-18}+{1,1,3}
177:n={0-18}+{1,2,3}
178:n={0-18}+{1,2,4}
179:n={0-18}+{1,2,5}
180:n={0-18}+{1,3,5}
Prove by list failed for n=17
Search for 17 elements
181:n={0-18}+{1,2,3,4}
182:n={0-18}+{1,2,3,5}
183:n={0-18}+{1,2,3,6}
184:n={0-18}+{1,2,4,6}
185:n={0-18}+{1,2,4,7}
186:n={0-18}+{1,1,2,4,7}
187:n={0-18}+{1,2,3,4,6}
188:n={0-18}+{1,2,3,4,7}
Prove by list failed for n=17
Search for 17 elements
189:n={0-18}+{1,2,3,5,7}
190:n={0-18}+{}
191:n={0-19}+{1}
Prove by list failed for n=18
Search for 18 elements
192:n={0-19}+{2}
193:n={0-19}+{1,2}
194:n={0-19}+{1,3}
195:n={0-19}+{1,1,3}
196:n={0-19}+{1,2,3}
197:n={0-19}+{1,2,4}
198:n={0-19}+{1,2,5}
Prove by list failed for n=18
Search for 18 elements
199:n={0-19}+{1,3,5}
200:n={0-19}+{1,2,3,4}
201:n={0-19}+{1,2,3,5}
202:n={0-19}+{1,2,3,6}
203:n={0-19}+{1,2,4,6}
204:n={0-19}+{1,1,2,4,6}
205:n={0-19}+{1,1,2,4,7}
206:n={0-19}+{1,2,3,4,6}
Prove by list failed for n=18
Search for 18 elements
207:n={0-19}+{1,2,3,4,7}
208:n={0-19}+{1,2,3,5,7}
209:n={0-19}+{1,2,3,5,8}
210:n={0-19}+{}
Prove by list failed for n=19
Search for 19 elements
211:n={0-20}+{1}
212:n={0-20}+{2}
213:n={0-20}+{1,2}
214:n={0-20}+{1,3}
215:n={0-20}+{1,1,3}
216:n={0-20}+{1,2,3}
217:n={0-20}+{1,2,4}
Prove by list failed for n=19
Search for 19 elements
218:n={0-20}+{1,1,2,4}
219:n={0-20}+{1,3,5}
220:n={0-20}+{1,2,3,4}
221:n={0-20}+{1,2,3,5}
222:n={0-20}+{1,2,3,6}
223:n={0-20}+{1,2,4,6}
224:n={0-20}+{1,1,2,4,6}
225:n={0-20}+{1,1,2,4,7}
Prove by list failed for n=19
Search for 19 elements
226:n={0-20}+{1,2,3,4,6}
227:n={0-20}+{1,2,3,4,7}
228:n={0-20}+{1,2,3,5,7}
229:n={0-20}+{1,2,3,5,8}
230:n={0-20}+{1,1,2,3,5,8}
Prove by list failed for n=20
Search for 20 elements
231:n={0-20}+{}
232:n={0-21}+{1}
233:n={0-21}+{2}
234:n={0-21}+{1,2}
235:n={0-21}+{1,3}
236:n={0-21}+{1,1,3}
237:n={0-21}+{1,2,3}
Prove by list failed for n=20
Search for 20 elements
238:n={0-21}+{1,2,4}
239:n={0-21}+{1,1,2,4}
240:n={0-21}+{1,3,5}
241:n={0-21}+{1,2,3,4}
242:n={0-21}+{1,2,3,5}
243:n={0-21}+{1,2,3,6}
244:n={0-21}+{1,2,4,6}
245:n={0-21}+{1,1,2,4,6}
Prove by list failed for n=20
Search for 20 elements
246:n={0-21}+{1,1,2,4,7}
247:n={0-21}+{1,2,3,4,6}
248:n={0-21}+{1,2,3,4,7}
249:n={0-21}+{1,2,3,5,7}
250:n={0-21}+{1,2,3,5,8}
251:n={0-21}+{1,1,2,3,5,8}
252:n={0-21}+{1,1,2,4,5,8}
253:n={0-21}+{}
254:n={0-22}+{1}
255:n={0-22}+{2}
256:n={0-22}+{1,2}
257:n={0-22}+{1,3}
258:n={0-22}+{1,1,3}
Prove by list failed for n=21
Search for 21 elements
259:n={0-22}+{1,2,3}
260:n={0-22}+{1,2,4}
261:n={0-22}+{1,1,2,4}
262:n={0-22}+{1,3,5}
263:n={0-22}+{1,2,3,4}
264:n={0-22}+{1,2,3,5}
265:n={0-22}+{1,2,3,6}
266:n={0-22}+{1,2,4,6}
Prove by list failed for n=21
Search for 21 elements
267:n={0-22}+{1,1,2,4,6}
268:n={0-22}+{1,1,2,4,7}
269:n={0-22}+{1,2,3,4,6}
270:n={0-22}+{1,2,3,4,7}
271:n={0-22}+{1,2,3,5,7}
272:n={0-22}+{1,2,3,5,8}
273:n={0-22}+{1,1,2,3,5,8}
274:n={0-22}+{1,1,2,4,5,8}
275:n={0-22}+{1,1,2,4,6,8}
276:n={0-22}+{}
277:n={0-23}+{1}
278:n={0-23}+{2}
279:n={0-23}+{1,2}
280:n={0-23}+{1,3}
Prove by list failed for n=22
Search for 22 elements
281:n={0-23}+{1,1,3}
282:n={0-23}+{1,2,3}
283:n={0-23}+{1,2,4}
284:n={0-23}+{1,1,2,4}
285:n={0-23}+{1,1,3,4}
286:n={0-23}+{1,2,3,4}
287:n={0-23}+{1,2,3,5}
288:n={0-23}+{1,2,3,6}
Prove by list failed for n=22
Search for 22 elements
289:n={0-23}+{1,2,4,6}
290:n={0-23}+{1,1,2,4,6}
291:n={0-23}+{1,1,3,4,6}
292:n={0-23}+{1,2,3,4,6}
293:n={0-23}+{1,2,3,4,7}
294:n={0-23}+{1,2,3,5,7}
295:n={0-23}+{1,2,3,5,8}
296:n={0-23}+{1,1,2,3,5,8}
297:n={0-23}+{1,1,2,4,5,8}
Prove by list failed for n=22
Search for 22 elements
298:n={0-23}+{1,1,2,4,6,8}
299:n={0-23}+{1,2,3,4,5,8}
300:n={0-23}+{}
301:n={0-24}+{1}
302:n={0-24}+{2}
303:n={0-24}+{1,2}
Prove by list failed for n=23
Search for 23 elements
304:n={0-24}+{1,3}
305:n={0-24}+{1,1,3}
306:n={0-24}+{1,2,3}
307:n={0-24}+{1,2,4}
308:n={0-24}+{1,1,2,4}
309:n={0-24}+{1,1,3,4}
310:n={0-24}+{1,2,3,4}
311:n={0-24}+{1,2,3,5}
Prove by list failed for n=23
Search for 23 elements
312:n={0-24}+{1,2,3,6}
313:n={0-24}+{1,2,4,6}
314:n={0-24}+{1,1,2,4,6}
315:n={0-24}+{1,1,3,4,6}
316:n={0-24}+{1,2,3,4,6}
317:n={0-24}+{1,2,3,4,7}
318:n={0-24}+{1,2,3,5,7}
319:n={0-24}+{1,2,3,5,8}
320:n={0-24}+{1,1,2,3,5,8}
Prove by list failed for n=23
Search for 23 elements
321:n={0-24}+{1,1,2,4,5,8}
322:n={0-24}+{1,2,3,4,5,7}
323:n={0-24}+{1,2,3,4,5,8}
324:n={0-24}+{1,2,3,4,6,8}
325:n={0-24}+{}
326:n={0-25}+{1}
327:n={0-25}+{2}
Prove by list failed for n=24
Search for 24 elements
328:n={0-25}+{1,2}
329:n={0-25}+{1,3}
330:n={0-25}+{1,1,3}
331:n={0-25}+{1,2,3}
332:n={0-25}+{1,2,4}
333:n={0-25}+{1,1,2,4}
334:n={0-25}+{1,1,3,4}
335:n={0-25}+{1,2,3,4}
Prove by list failed for n=24
Search for 24 elements
336:n={0-25}+{1,2,3,5}
337:n={0-25}+{1,2,3,6}
338:n={0-25}+{1,2,4,6}
339:n={0-25}+{1,1,2,4,6}
340:n={0-25}+{1,1,3,4,6}
341:n={0-25}+{1,2,3,4,6}
342:n={0-25}+{1,2,3,4,7}
343:n={0-25}+{1,2,3,5,7}
344:n={0-25}+{1,1,2,3,5,7}
Prove by list failed for n=24
Search for 24 elements
345:n={0-25}+{1,1,2,3,5,8}
346:n={0-25}+{1,1,2,4,5,8}
347:n={0-25}+{1,2,3,4,5,7}
348:n={0-25}+{1,2,3,4,5,8}
349:n={0-25}+{1,2,3,4,6,8}
350:n={0-25}+{1,2,3,4,6,9}
351:n={0-25}+{}
352:n={0-26}+{1}
Prove by list failed for n=25
Search for 25 elements
353:n={0-26}+{2}
354:n={0-26}+{1,2}
355:n={0-26}+{1,3}
356:n={0-26}+{1,1,3}
357:n={0-26}+{1,2,3}
358:n={0-26}+{1,2,4}
359:n={0-26}+{1,1,2,4}
360:n={0-26}+{1,1,3,4}
Prove by list failed for n=25
Search for 25 elements
361:n={0-26}+{1,2,3,4}
362:n={0-26}+{1,2,3,5}
363:n={0-26}+{1,2,3,6}
364:n={0-26}+{1,2,4,6}
365:n={0-26}+{1,1,2,4,6}
366:n={0-26}+{1,1,3,4,6}
367:n={0-26}+{1,2,3,4,6}
368:n={0-26}+{1,2,3,4,7}
369:n={0-26}+{1,2,3,5,7}
Prove by list failed for n=25
Search for 25 elements
370:n={0-26}+{1,1,2,3,5,7}
371:n={0-26}+{1,1,2,3,5,8}
372:n={0-26}+{1,1,2,4,5,8}
373:n={0-26}+{1,2,3,4,5,7}
374:n={0-26}+{1,2,3,4,5,8}
375:n={0-26}+{1,2,3,4,6,8}
376:n={0-26}+{1,2,3,4,6,9}
377:n={0-26}+{1,1,2,3,4,6,9}
378:n={0-26}+{}
Prove by list failed for n=26
Search for 26 elements
379:n={0-27}+{1}
380:n={0-27}+{2}
381:n={0-27}+{1,2}
382:n={0-27}+{1,3}
383:n={0-27}+{1,1,3}
384:n={0-27}+{1,2,3}
385:n={0-27}+{1,2,4}
386:n={0-27}+{1,1,2,4}
Prove by list failed for n=26
Search for 26 elements
387:n={0-27}+{1,1,3,4}
388:n={0-27}+{1,2,3,4}
389:n={0-27}+{1,2,3,5}
390:n={0-27}+{1,2,3,6}
391:n={0-27}+{1,2,4,6}
392:n={0-27}+{1,1,2,4,6}
393:n={0-27}+{1,1,3,4,6}
394:n={0-27}+{1,2,3,4,6}
395:n={0-27}+{1,2,3,4,7}
Prove by list failed for n=26
Search for 26 elements
396:n={0-27}+{1,2,3,5,7}
397:n={0-27}+{1,1,2,3,5,7}
398:n={0-27}+{1,1,2,3,5,8}
399:n={0-27}+{1,1,2,4,5,8}
400:n={0-27}+{1,2,3,4,5,7}
401:n={0-27}+{1,2,3,4,5,8}
402:n={0-27}+{1,2,3,4,6,8}
403:n={0-27}+{1,2,3,4,6,9}
404:n={0-27}+{1,1,2,3,4,6,9}
405:n={0-27}+{1,1,2,3,5,6,9}
Prove by list failed for n=27
Search for 27 elements
406:n={0-27}+{}
407:n={0-28}+{1}
408:n={0-28}+{2}
409:n={0-28}+{1,2}
410:n={0-28}+{1,3}
411:n={0-28}+{1,1,3}
412:n={0-28}+{1,2,3}
413:n={0-28}+{1,2,4}
Prove by list failed for n=27
Search for 27 elements
414:n={0-28}+{1,1,2,4}
415:n={0-28}+{1,1,3,4}
416:n={0-28}+{1,2,3,4}
417:n={0-28}+{1,2,3,5}
418:n={0-28}+{1,1,2,3,5}
419:n={0-28}+{1,2,4,6}
420:n={0-28}+{1,1,2,4,6}
421:n={0-28}+{1,2,3,4,5}
422:n={0-28}+{1,2,3,4,6}
Prove by list failed for n=27
Search for 27 elements
423:n={0-28}+{1,2,3,4,7}
424:n={0-28}+{1,2,3,5,7}
425:n={0-28}+{1,1,2,3,5,7}
426:n={0-28}+{1,1,2,3,5,8}
427:n={0-28}+{1,1,2,4,5,8}
428:n={0-28}+{1,2,3,4,5,7}
429:n={0-28}+{1,2,3,4,5,8}
430:n={0-28}+{1,2,3,4,6,8}
431:n={0-28}+{1,2,3,4,6,9}
432:n={0-28}+{1,1,2,3,4,6,9}
Prove by list failed for n=27
Search for 27 elements
433:n={0-28}+{1,1,2,3,5,6,9}
434:n={0-28}+{1,1,2,3,5,7,9}
435:n={0-28}+{}
436:n={0-29}+{1}
437:n={0-29}+{2}
438:n={0-29}+{1,2}
439:n={0-29}+{1,3}
440:n={0-29}+{1,1,3}
441:n={0-29}+{1,2,3}
Prove by list failed for n=28
Search for 28 elements
442:n={0-29}+{1,2,4}
443:n={0-29}+{1,1,2,4}
444:n={0-29}+{1,1,3,4}
445:n={0-29}+{1,2,3,4}
446:n={0-29}+{1,2,3,5}
447:n={0-29}+{1,1,2,3,5}
448:n={0-29}+{1,2,4,6}
449:n={0-29}+{1,1,2,4,6}
450:n={0-29}+{1,2,3,4,5}
Prove by list failed for n=28
Search for 28 elements
451:n={0-29}+{1,2,3,4,6}
452:n={0-29}+{1,2,3,4,7}
453:n={0-29}+{1,2,3,5,7}
454:n={0-29}+{1,1,2,3,5,7}
455:n={0-29}+{1,1,2,3,5,8}
456:n={0-29}+{1,1,2,4,5,8}
457:n={0-29}+{1,2,3,4,5,7}
458:n={0-29}+{1,2,3,4,5,8}
459:n={0-29}+{1,2,3,4,6,8}
460:n={0-29}+{1,2,3,4,6,9}
Prove by list failed for n=28
Search for 28 elements
461:n={0-29}+{1,1,2,3,4,6,9}
462:n={0-29}+{1,1,2,3,5,6,9}
463:n={0-29}+{1,1,2,3,5,7,9}
464:n={0-29}+{1,1,2,3,5,7,10}
465:n={0-29}+{}
466:n={0-30}+{1}
467:n={0-30}+{2}
468:n={0-30}+{1,2}
469:n={0-30}+{1,3}
470:n={0-30}+{1,1,3}
Prove by list failed for n=29
Search for 29 elements
471:n={0-30}+{1,2,3}
472:n={0-30}+{1,2,4}
473:n={0-30}+{1,1,2,4}
474:n={0-30}+{1,1,3,4}
475:n={0-30}+{1,2,3,4}
476:n={0-30}+{1,2,3,5}
477:n={0-30}+{1,1,2,3,5}
478:n={0-30}+{1,2,4,6}
479:n={0-30}+{1,1,2,4,6}
Prove by list failed for n=29
Search for 29 elements
480:n={0-30}+{1,2,3,4,5}
481:n={0-30}+{1,2,3,4,6}
482:n={0-30}+{1,2,3,4,7}
483:n={0-30}+{1,2,3,5,7}
484:n={0-30}+{1,1,2,3,5,7}
485:n={0-30}+{1,1,2,3,5,8}
486:n={0-30}+{1,1,2,4,5,8}
487:n={0-30}+{1,2,3,4,5,7}
488:n={0-30}+{1,2,3,4,5,8}
489:n={0-30}+{1,2,3,4,6,8}
Prove by list failed for n=29
Search for 29 elements
490:n={0-30}+{1,2,3,4,6,9}
491:n={0-30}+{1,1,2,3,4,6,9}
492:n={0-30}+{1,1,2,3,5,6,9}
493:n={0-30}+{1,1,2,3,5,7,9}
494:n={0-30}+{1,1,2,3,5,7,10}
495:n={0-30}+{1,2,3,4,5,6,9}
496:n={0-30}+{}
497:n={0-31}+{1}
498:n={0-31}+{2}
499:n={0-31}+{1,2}
500:n={0-31}+{1,3}
Prove by list failed for n=30
Search for 30 elements
501:n={0-31}+{1,1,3}
502:n={0-31}+{1,2,3}
503:n={0-31}+{1,2,4}
504:n={0-31}+{1,1,2,4}
505:n={0-31}+{1,1,3,4}
506:n={0-31}+{1,2,3,4}
507:n={0-31}+{1,2,3,5}
508:n={0-31}+{1,1,2,3,5}
509:n={0-31}+{1,2,4,6}
Prove by list failed for n=30
Search for 30 elements
510:n={0-31}+{1,1,2,4,6}
511:n={0-31}+{1,2,3,4,5}
512:n={0-31}+{1,2,3,4,6}
513:n={0-31}+{1,2,3,4,7}
514:n={0-31}+{1,2,3,5,7}
515:n={0-31}+{1,1,2,3,5,7}
516:n={0-31}+{1,1,2,3,5,8}
517:n={0-31}+{1,1,2,4,5,8}
518:n={0-31}+{1,2,3,4,5,7}
519:n={0-31}+{1,2,3,4,5,8}
Prove by list failed for n=30
Search for 30 elements
520:n={0-31}+{1,2,3,4,6,8}
521:n={0-31}+{1,1,2,3,4,6,8}
522:n={0-31}+{1,1,2,3,4,6,9}
523:n={0-31}+{1,1,2,3,5,6,9}
524:n={0-31}+{1,1,2,3,5,7,9}
525:n={0-31}+{1,1,2,3,5,7,10}
526:n={0-31}+{1,2,3,4,5,6,9}
527:n={0-31}+{1,2,3,4,5,7,9}
528:n={0-31}+{}
529:n={0-32}+{1}
530:n={0-32}+{2}
531:n={0-32}+{1,2}
Prove by list failed for n=31
Search for 31 elements
532:n={0-32}+{1,3}
533:n={0-32}+{1,1,3}
534:n={0-32}+{1,2,3}
535:n={0-32}+{1,2,4}
536:n={0-32}+{1,1,2,4}
537:n={0-32}+{1,1,3,4}
538:n={0-32}+{1,2,3,4}
539:n={0-32}+{1,2,3,5}
540:n={0-32}+{1,1,2,3,5}
Prove by list failed for n=31
Search for 31 elements
541:n={0-32}+{1,2,4,6}
542:n={0-32}+{1,1,2,4,6}
543:n={0-32}+{1,2,3,4,5}
544:n={0-32}+{1,2,3,4,6}
545:n={0-32}+{1,2,3,4,7}
546:n={0-32}+{1,2,3,5,7}
547:n={0-32}+{1,1,2,3,5,7}
548:n={0-32}+{1,1,2,3,5,8}
549:n={0-32}+{1,1,2,4,5,8}
550:n={0-32}+{1,2,3,4,5,7}
Prove by list failed for n=31
Search for 31 elements
551:n={0-32}+{1,2,3,4,5,8}
552:n={0-32}+{1,2,3,4,6,8}
553:n={0-32}+{1,1,2,3,4,6,8}
554:n={0-32}+{1,1,2,3,4,6,9}
555:n={0-32}+{1,1,2,3,5,6,9}
556:n={0-32}+{1,1,2,3,5,7,9}
557:n={0-32}+{1,1,2,3,5,7,10}
558:n={0-32}+{1,2,3,4,5,6,9}
559:n={0-32}+{1,2,3,4,5,7,9}
560:n={0-32}+{1,2,3,4,5,7,10}
561:n={0-32}+{}
562:n={0-33}+{1}
563:n={0-33}+{2}
Prove by list failed for n=32
Search for 32 elements
564:n={0-33}+{1,2}
565:n={0-33}+{1,3}
566:n={0-33}+{1,1,3}
567:n={0-33}+{1,2,3}
568:n={0-33}+{1,2,4}
569:n={0-33}+{1,1,2,4}
570:n={0-33}+{1,1,3,4}
571:n={0-33}+{1,2,3,4}
572:n={0-33}+{1,2,3,5}
Prove by list failed for n=32
Search for 32 elements
573:n={0-33}+{1,1,2,3,5}
574:n={0-33}+{1,1,2,3,6}
575:n={0-33}+{1,1,2,4,6}
576:n={0-33}+{1,2,3,4,5}
577:n={0-33}+{1,2,3,4,6}
578:n={0-33}+{1,2,3,4,7}
579:n={0-33}+{1,2,3,5,7}
580:n={0-33}+{1,1,2,3,5,7}
581:n={0-33}+{1,1,2,3,5,8}
582:n={0-33}+{1,1,2,4,5,8}
Prove by list failed for n=32
Search for 32 elements
583:n={0-33}+{1,2,3,4,5,7}
584:n={0-33}+{1,2,3,4,5,8}
585:n={0-33}+{1,2,3,4,6,8}
586:n={0-33}+{1,1,2,3,4,6,8}
587:n={0-33}+{1,1,2,3,4,6,9}
588:n={0-33}+{1,1,2,3,5,6,9}
589:n={0-33}+{1,1,2,3,5,7,9}
590:n={0-33}+{1,1,2,3,5,7,10}
591:n={0-33}+{1,2,3,4,5,6,9}
592:n={0-33}+{1,2,3,4,5,7,9}
593:n={0-33}+{1,2,3,4,5,7,10}
Prove by list failed for n=32
Search for 32 elements
594:n={0-33}+{1,1,2,3,4,5,7,10}
595:n={0-33}+{}
596:n={0-34}+{1}
Prove by list failed for n=33
Search for 33 elements
597:n={0-34}+{2}
598:n={0-34}+{1,2}
599:n={0-34}+{1,3}
600:n={0-34}+{1,1,3}
601:n={0-34}+{1,2,3}
602:n={0-34}+{1,2,4}
603:n={0-34}+{1,1,2,4}
604:n={0-34}+{1,1,3,4}
605:n={0-34}+{1,2,3,4}
Prove by list failed for n=33
Search for 33 elements
606:n={0-34}+{1,2,3,5}
607:n={0-34}+{1,1,2,3,5}
608:n={0-34}+{1,1,2,3,6}
609:n={0-34}+{1,1,2,4,6}
610:n={0-34}+{1,2,3,4,5}
611:n={0-34}+{1,2,3,4,6}
612:n={0-34}+{1,2,3,4,7}
613:n={0-34}+{1,2,3,5,7}
614:n={0-34}+{1,1,2,3,5,7}
615:n={0-34}+{1,1,2,3,5,8}
Prove by list failed for n=33
Search for 33 elements
616:n={0-34}+{1,1,2,4,5,8}
617:n={0-34}+{1,2,3,4,5,7}
618:n={0-34}+{1,2,3,4,5,8}
619:n={0-34}+{1,2,3,4,6,8}
620:n={0-34}+{1,1,2,3,4,6,8}
621:n={0-34}+{1,1,2,3,4,6,9}
622:n={0-34}+{1,1,2,3,5,6,9}
623:n={0-34}+{1,1,2,3,5,7,9}
624:n={0-34}+{1,1,2,3,5,7,10}
625:n={0-34}+{1,2,3,4,5,6,9}
626:n={0-34}+{1,2,3,4,5,7,9}
Prove by list failed for n=33
Search for 33 elements
627:n={0-34}+{1,2,3,4,5,7,10}
628:n={0-34}+{1,1,2,3,4,5,7,10}
629:n={0-34}+{1,1,2,3,4,6,7,10}
630:n={0-34}+{}
Prove by list failed for n=34
Search for 34 elements
631:n={0-35}+{1}
632:n={0-35}+{2}
633:n={0-35}+{1,2}
634:n={0-35}+{1,3}
635:n={0-35}+{1,1,3}
636:n={0-35}+{1,2,3}
637:n={0-35}+{1,2,4}
638:n={0-35}+{1,1,2,4}
639:n={0-35}+{1,1,3,4}
640:n={0-35}+{1,2,3,4}
641:n={0-35}+{1,2,3,5}
642:n={0-35}+{1,1,2,3,5}
643:n={0-35}+{1,1,2,3,6}
644:n={0-35}+{1,1,2,4,6}
645:n={0-35}+{1,2,3,4,5}
646:n={0-35}+{1,2,3,4,6}
647:n={0-35}+{1,2,3,4,7}
648:n={0-35}+{1,2,3,5,7}
649:n={0-35}+{1,1,2,3,5,7}
Prove by list failed for n=34
Search for 34 elements
650:n={0-35}+{1,1,2,3,5,8}
651:n={0-35}+{1,1,2,4,5,8}
652:n={0-35}+{1,2,3,4,5,7}
653:n={0-35}+{1,2,3,4,5,8}
654:n={0-35}+{1,2,3,4,6,8}
655:n={0-35}+{1,1,2,3,4,6,8}
656:n={0-35}+{1,1,2,3,4,6,9}
657:n={0-35}+{1,1,2,3,5,6,9}
658:n={0-35}+{1,1,2,3,5,7,9}
659:n={0-35}+{1,1,2,3,5,7,10}
660:n={0-35}+{1,2,3,4,5,6,9}
Prove by list failed for n=34
Search for 34 elements
661:n={0-35}+{1,2,3,4,5,7,9}
662:n={0-35}+{1,2,3,4,5,7,10}
663:n={0-35}+{1,1,2,3,4,5,7,10}
664:n={0-35}+{1,1,2,3,4,6,7,10}
665:n={0-35}+{1,1,2,3,4,6,8,10}
Prove by list failed for n=35
Search for 35 elements
666:n={0-35}+{}
667:n={0-36}+{1}
668:n={0-36}+{2}
669:n={0-36}+{1,2}
670:n={0-36}+{1,3}
671:n={0-36}+{1,1,3}
672:n={0-36}+{1,2,3}
673:n={0-36}+{1,2,4}
674:n={0-36}+{1,1,2,4}
675:n={0-36}+{1,1,3,4}
676:n={0-36}+{1,2,3,4}
677:n={0-36}+{1,2,3,5}
678:n={0-36}+{1,1,2,3,5}
679:n={0-36}+{1,1,2,3,6}
680:n={0-36}+{1,1,2,4,6}
681:n={0-36}+{1,2,3,4,5}
682:n={0-36}+{1,2,3,4,6}
683:n={0-36}+{1,1,2,3,4,6}
684:n={0-36}+{1,2,3,5,7}
Prove by list failed for n=35
Search for 35 elements
685:n={0-36}+{1,1,2,3,5,7}
686:n={0-36}+{1,1,2,3,5,8}
687:n={0-36}+{1,1,2,4,5,8}
688:n={0-36}+{1,2,3,4,5,7}
689:n={0-36}+{1,2,3,4,5,8}
690:n={0-36}+{1,2,3,4,6,8}
691:n={0-36}+{1,1,2,3,4,6,8}
692:n={0-36}+{1,1,2,3,4,6,9}
693:n={0-36}+{1,1,2,3,5,6,9}
694:n={0-36}+{1,1,2,3,5,7,9}
695:n={0-36}+{1,1,2,3,5,7,10}
Prove by list failed for n=35
Search for 35 elements
696:n={0-36}+{1,2,3,4,5,6,9}
697:n={0-36}+{1,2,3,4,5,7,9}
698:n={0-36}+{1,2,3,4,5,7,10}
699:n={0-36}+{1,1,2,3,4,5,7,10}
700:n={0-36}+{1,1,2,3,4,6,7,10}
701:n={0-36}+{1,1,2,3,4,6,8,10}
702:n={0-36}+{1,1,2,3,4,6,8,11}
703:n={0-36}+{}
704:n={0-37}+{1}
705:n={0-37}+{2}
706:n={0-37}+{1,2}
707:n={0-37}+{1,3}
708:n={0-37}+{1,1,3}
709:n={0-37}+{1,2,3}
710:n={0-37}+{1,2,4}
711:n={0-37}+{1,1,2,4}
712:n={0-37}+{1,1,3,4}
713:n={0-37}+{1,2,3,4}
714:n={0-37}+{1,2,3,5}
715:n={0-37}+{1,1,2,3,5}
716:n={0-37}+{1,1,2,3,6}
717:n={0-37}+{1,1,2,4,6}
718:n={0-37}+{1,2,3,4,5}
719:n={0-37}+{1,2,3,4,6}
720:n={0-37}+{1,1,2,3,4,6}
Prove by list failed for n=36
Search for 36 elements
721:n={0-37}+{1,2,3,5,7}
722:n={0-37}+{1,1,2,3,5,7}
723:n={0-37}+{1,1,2,3,5,8}
724:n={0-37}+{1,1,2,4,5,8}
725:n={0-37}+{1,2,3,4,5,7}
726:n={0-37}+{1,2,3,4,5,8}
727:n={0-37}+{1,2,3,4,6,8}
728:n={0-37}+{1,1,2,3,4,6,8}
729:n={0-37}+{1,1,2,3,4,6,9}
730:n={0-37}+{1,1,2,3,5,6,9}
731:n={0-37}+{1,1,2,3,5,7,9}
Prove by list failed for n=36
Search for 36 elements
732:n={0-37}+{1,1,2,3,5,7,10}
733:n={0-37}+{1,2,3,4,5,6,9}
734:n={0-37}+{1,2,3,4,5,7,9}
735:n={0-37}+{1,1,2,3,4,5,7,9}
736:n={0-37}+{1,1,2,3,4,5,7,10}
737:n={0-37}+{1,1,2,3,4,6,7,10}
738:n={0-37}+{1,1,2,3,4,6,8,10}
739:n={0-37}+{1,1,2,3,4,6,8,11}
740:n={0-37}+{1,1,2,3,5,6,8,11}
741:n={0-37}+{}
742:n={0-38}+{1}
743:n={0-38}+{2}
744:n={0-38}+{1,2}
745:n={0-38}+{1,3}
746:n={0-38}+{1,1,3}
747:n={0-38}+{1,2,3}
748:n={0-38}+{1,2,4}
749:n={0-38}+{1,1,2,4}
750:n={0-38}+{1,1,3,4}
751:n={0-38}+{1,2,3,4}
752:n={0-38}+{1,2,3,5}
753:n={0-38}+{1,1,2,3,5}
754:n={0-38}+{1,1,2,3,6}
755:n={0-38}+{1,1,2,4,6}
756:n={0-38}+{1,2,3,4,5}
757:n={0-38}+{1,2,3,4,6}
Prove by list failed for n=37
Search for 37 elements
758:n={0-38}+{1,1,2,3,4,6}
759:n={0-38}+{1,2,3,5,7}
760:n={0-38}+{1,1,2,3,5,7}
761:n={0-38}+{1,1,2,3,5,8}
762:n={0-38}+{1,1,2,4,5,8}
763:n={0-38}+{1,2,3,4,5,7}
764:n={0-38}+{1,2,3,4,5,8}
765:n={0-38}+{1,2,3,4,6,8}
766:n={0-38}+{1,1,2,3,4,6,8}
767:n={0-38}+{1,1,2,3,4,6,9}
768:n={0-38}+{1,1,2,3,5,6,9}
Prove by list failed for n=37
Search for 37 elements
769:n={0-38}+{1,1,2,3,5,7,9}
770:n={0-38}+{1,1,2,3,5,7,10}
771:n={0-38}+{1,2,3,4,5,6,9}
772:n={0-38}+{1,2,3,4,5,7,9}
773:n={0-38}+{1,1,2,3,4,5,7,9}
774:n={0-38}+{1,1,2,3,4,5,7,10}
775:n={0-38}+{1,1,2,3,4,6,7,10}
776:n={0-38}+{1,1,2,3,4,6,8,10}
777:n={0-38}+{1,1,2,3,4,6,8,11}
778:n={0-38}+{1,1,2,3,5,6,8,11}
779:n={0-38}+{1,1,2,2,3,4,6,8,11}
780:n={0-38}+{}
781:n={0-39}+{1}
782:n={0-39}+{2}
783:n={0-39}+{1,2}
784:n={0-39}+{1,3}
785:n={0-39}+{1,1,3}
786:n={0-39}+{1,2,3}
787:n={0-39}+{1,2,4}
788:n={0-39}+{1,1,2,4}
789:n={0-39}+{1,1,3,4}
790:n={0-39}+{1,2,3,4}
791:n={0-39}+{1,2,3,5}
792:n={0-39}+{1,1,2,3,5}
793:n={0-39}+{1,1,2,3,6}
794:n={0-39}+{1,1,2,4,6}
795:n={0-39}+{1,2,3,4,5}
796:n={0-39}+{1,2,3,4,6}
797:n={0-39}+{1,1,2,3,4,6}
798:n={0-39}+{1,2,3,5,7}
799:n={0-39}+{1,1,2,3,5,7}
800:n={0-39}+{1,1,2,3,5,8}
801:n={0-39}+{1,1,2,4,5,8}
802:n={0-39}+{1,2,3,4,5,7}
803:n={0-39}+{1,2,3,4,5,8}
804:n={0-39}+{1,2,3,4,6,8}
805:n={0-39}+{1,1,2,3,4,6,8}
806:n={0-39}+{1,1,2,3,4,6,9}
Prove by list failed for n=38
Search for 38 elements
807:n={0-39}+{1,1,2,3,5,6,9}
808:n={0-39}+{1,1,2,3,5,7,9}
809:n={0-39}+{1,1,2,3,5,7,10}
810:n={0-39}+{1,2,3,4,5,6,9}
811:n={0-39}+{1,2,3,4,5,7,9}
812:n={0-39}+{1,1,2,3,4,5,7,9}
813:n={0-39}+{1,1,2,3,4,5,7,10}
814:n={0-39}+{1,1,2,3,4,6,7,10}
815:n={0-39}+{1,1,2,3,4,6,8,10}
816:n={0-39}+{1,1,2,3,4,6,8,11}
817:n={0-39}+{1,1,2,3,5,6,8,11}
818:n={0-39}+{1,1,2,2,3,4,6,8,11}
Prove by list failed for n=38
Search for 38 elements
819:n={0-39}+{1,2,3,4,5,6,8,10}
820:n={0-39}+{}
821:n={0-40}+{1}
822:n={0-40}+{2}
823:n={0-40}+{1,2}
824:n={0-40}+{1,3}
825:n={0-40}+{1,1,3}
826:n={0-40}+{1,2,3}
827:n={0-40}+{1,2,4}
828:n={0-40}+{1,1,2,4}
829:n={0-40}+{1,1,3,4}
830:n={0-40}+{1,2,3,4}
831:n={0-40}+{1,2,3,5}
832:n={0-40}+{1,1,2,3,5}
833:n={0-40}+{1,1,2,3,6}
834:n={0-40}+{1,1,2,4,6}
835:n={0-40}+{1,2,3,4,5}
836:n={0-40}+{1,2,3,4,6}
837:n={0-40}+{1,1,2,3,4,6}
838:n={0-40}+{1,1,2,3,4,7}
839:n={0-40}+{1,1,2,3,5,7}
840:n={0-40}+{1,1,2,3,5,8}
841:n={0-40}+{1,1,2,4,5,8}
842:n={0-40}+{1,2,3,4,5,7}
843:n={0-40}+{1,2,3,4,5,8}
844:n={0-40}+{1,2,3,4,6,8}
845:n={0-40}+{1,1,2,3,4,6,8}
Prove by list failed for n=39
Search for 39 elements
846:n={0-40}+{1,1,2,3,4,6,9}
847:n={0-40}+{1,1,2,3,5,6,9}
848:n={0-40}+{1,1,2,3,5,7,9}
849:n={0-40}+{1,1,2,3,5,7,10}
850:n={0-40}+{1,2,3,4,5,6,9}
851:n={0-40}+{1,2,3,4,5,7,9}
852:n={0-40}+{1,1,2,3,4,5,7,9}
853:n={0-40}+{1,1,2,3,4,5,7,10}
854:n={0-40}+{1,1,2,3,4,6,7,10}
855:n={0-40}+{1,1,2,3,4,6,8,10}
856:n={0-40}+{1,1,2,3,4,6,8,11}
857:n={0-40}+{1,1,2,3,5,6,8,11}
Prove by list failed for n=39
Search for 39 elements
858:n={0-40}+{1,1,2,2,3,4,6,8,11}
859:n={0-40}+{1,2,3,4,5,6,8,10}
860:n={0-40}+{1,2,3,4,5,6,8,11}
861:n={0-40}+{}
862:n={0-41}+{1}
863:n={0-41}+{2}
864:n={0-41}+{1,2}
865:n={0-41}+{1,3}
866:n={0-41}+{1,1,3}
867:n={0-41}+{1,2,3}
868:n={0-41}+{1,2,4}
869:n={0-41}+{1,1,2,4}
870:n={0-41}+{1,1,3,4}
871:n={0-41}+{1,2,3,4}
872:n={0-41}+{1,2,3,5}
873:n={0-41}+{1,1,2,3,5}
874:n={0-41}+{1,1,2,3,6}
875:n={0-41}+{1,1,2,4,6}
876:n={0-41}+{1,2,3,4,5}
877:n={0-41}+{1,2,3,4,6}
878:n={0-41}+{1,1,2,3,4,6}
879:n={0-41}+{1,1,2,3,4,7}
880:n={0-41}+{1,1,2,3,5,7}
881:n={0-41}+{1,1,2,3,5,8}
882:n={0-41}+{1,1,2,4,5,8}
883:n={0-41}+{1,2,3,4,5,7}
884:n={0-41}+{1,2,3,4,5,8}
885:n={0-41}+{1,2,3,4,6,8}
Prove by list failed for n=40
Search for 40 elements
886:n={0-41}+{1,1,2,3,4,6,8}
887:n={0-41}+{1,1,2,3,4,6,9}
888:n={0-41}+{1,1,2,3,5,6,9}
889:n={0-41}+{1,1,2,3,5,7,9}
890:n={0-41}+{1,1,2,3,5,7,10}
891:n={0-41}+{1,2,3,4,5,6,9}
892:n={0-41}+{1,2,3,4,5,7,9}
893:n={0-41}+{1,1,2,3,4,5,7,9}
894:n={0-41}+{1,1,2,3,4,5,7,10}
895:n={0-41}+{1,1,2,3,4,6,7,10}
896:n={0-41}+{1,1,2,3,4,6,8,10}
897:n={0-41}+{1,1,2,3,4,6,8,11}
Prove by list failed for n=40
Search for 40 elements
898:n={0-41}+{1,1,2,3,5,6,8,11}
899:n={0-41}+{1,1,2,2,3,4,6,8,11}
900:n={0-41}+{1,2,3,4,5,6,8,10}
901:n={0-41}+{1,2,3,4,5,6,8,11}
902:n={0-41}+{1,1,2,3,4,5,6,8,11}
903:n={0-41}+{}
904:n={0-42}+{1}
905:n={0-42}+{2}
906:n={0-42}+{1,2}
907:n={0-42}+{1,3}
908:n={0-42}+{1,1,3}
909:n={0-42}+{1,2,3}
910:n={0-42}+{1,2,4}
911:n={0-42}+{1,1,2,4}
912:n={0-42}+{1,1,3,4}
913:n={0-42}+{1,2,3,4}
914:n={0-42}+{1,2,3,5}
915:n={0-42}+{1,1,2,3,5}
916:n={0-42}+{1,1,2,3,6}
917:n={0-42}+{1,1,2,4,6}
918:n={0-42}+{1,2,3,4,5}
919:n={0-42}+{1,2,3,4,6}
920:n={0-42}+{1,1,2,3,4,6}
921:n={0-42}+{1,1,2,3,4,7}
922:n={0-42}+{1,1,2,3,5,7}
923:n={0-42}+{1,1,2,3,5,8}
924:n={0-42}+{1,1,2,4,5,8}
925:n={0-42}+{1,2,3,4,5,7}
926:n={0-42}+{1,2,3,4,5,8}
Prove by list failed for n=41
Search for 41 elements
927:n={0-42}+{1,2,3,4,6,8}
928:n={0-42}+{1,1,2,3,4,6,8}
929:n={0-42}+{1,1,2,3,4,6,9}
930:n={0-42}+{1,1,2,3,5,6,9}
931:n={0-42}+{1,1,2,3,5,7,9}
932:n={0-42}+{1,2,3,4,5,6,8}
933:n={0-42}+{1,2,3,4,5,6,9}
934:n={0-42}+{1,2,3,4,5,7,9}
935:n={0-42}+{1,1,2,3,4,5,7,9}
936:n={0-42}+{1,1,2,3,4,5,7,10}
937:n={0-42}+{1,1,2,3,4,6,7,10}
938:n={0-42}+{1,1,2,3,4,6,8,10}
Prove by list failed for n=41
Search for 41 elements
939:n={0-42}+{1,1,2,3,4,6,8,11}
940:n={0-42}+{1,1,2,3,5,6,8,11}
941:n={0-42}+{1,1,2,2,3,4,6,8,11}
942:n={0-42}+{1,2,3,4,5,6,8,10}
943:n={0-42}+{1,2,3,4,5,6,8,11}
944:n={0-42}+{1,1,2,3,4,5,6,8,11}
945:n={0-42}+{1,1,2,3,4,5,7,8,11}
946:n={0-42}+{}
947:n={0-43}+{1}
948:n={0-43}+{2}
949:n={0-43}+{1,2}
950:n={0-43}+{1,3}
951:n={0-43}+{1,1,3}
952:n={0-43}+{1,2,3}
953:n={0-43}+{1,2,4}
954:n={0-43}+{1,1,2,4}
955:n={0-43}+{1,1,3,4}
956:n={0-43}+{1,2,3,4}
957:n={0-43}+{1,2,3,5}
958:n={0-43}+{1,1,2,3,5}
959:n={0-43}+{1,1,2,3,6}
960:n={0-43}+{1,1,2,4,6}
961:n={0-43}+{1,2,3,4,5}
962:n={0-43}+{1,2,3,4,6}
963:n={0-43}+{1,1,2,3,4,6}
964:n={0-43}+{1,1,2,3,4,7}
965:n={0-43}+{1,1,2,3,5,7}
966:n={0-43}+{1,1,2,3,5,8}
967:n={0-43}+{1,1,2,4,5,8}
968:n={0-43}+{1,2,3,4,5,7}
Prove by list failed for n=42
Search for 42 elements
969:n={0-43}+{1,2,3,4,5,8}
970:n={0-43}+{1,2,3,4,6,8}
971:n={0-43}+{1,1,2,3,4,6,8}
972:n={0-43}+{1,1,2,3,4,6,9}
973:n={0-43}+{1,1,2,3,5,6,9}
974:n={0-43}+{1,1,2,3,5,7,9}
975:n={0-43}+{1,2,3,4,5,6,8}
976:n={0-43}+{1,2,3,4,5,6,9}
977:n={0-43}+{1,2,3,4,5,7,9}
978:n={0-43}+{1,1,2,3,4,5,7,9}
979:n={0-43}+{1,1,2,3,4,5,7,10}
980:n={0-43}+{1,1,2,3,4,6,7,10}
Prove by list failed for n=42
Search for 42 elements
981:n={0-43}+{1,1,2,3,4,6,8,10}
982:n={0-43}+{1,1,2,3,4,6,8,11}
983:n={0-43}+{1,1,2,3,5,6,8,11}
984:n={0-43}+{1,1,2,2,3,4,6,8,11}
985:n={0-43}+{1,2,3,4,5,6,8,10}
986:n={0-43}+{1,1,2,3,4,5,6,8,10}
987:n={0-43}+{1,1,2,3,4,5,6,8,11}
988:n={0-43}+{1,1,2,3,4,5,7,8,11}
989:n={0-43}+{1,1,2,3,4,5,7,9,11}
990:n={0-43}+{}
991:n={0-44}+{1}
992:n={0-44}+{2}
993:n={0-44}+{1,2}
994:n={0-44}+{1,3}
995:n={0-44}+{1,1,3}
996:n={0-44}+{1,2,3}
997:n={0-44}+{1,2,4}
998:n={0-44}+{1,1,2,4}
999:n={0-44}+{1,1,3,4}
1000:n={0-44}+{1,2,3,4}
1001:n={0-44}+{1,2,3,5}
1002:n={0-44}+{1,1,2,3,5}
1003:n={0-44}+{1,1,2,3,6}
1004:n={0-44}+{1,1,2,4,6}
1005:n={0-44}+{1,2,3,4,5}
1006:n={0-44}+{1,2,3,4,6}
1007:n={0-44}+{1,1,2,3,4,6}
1008:n={0-44}+{1,1,2,3,4,7}
1009:n={0-44}+{1,1,2,3,5,7}
1010:n={0-44}+{1,1,2,3,5,8}
1011:n={0-44}+{1,2,2,4,5,7}
Prove by list failed for n=43
Search for 43 elements
1012:n={0-44}+{1,2,3,4,5,7}
1013:n={0-44}+{1,2,3,4,5,8}
1014:n={0-44}+{1,2,3,4,6,8}
1015:n={0-44}+{1,1,2,3,4,6,8}
1016:n={0-44}+{1,1,2,3,4,6,9}
1017:n={0-44}+{1,1,2,3,5,6,9}
1018:n={0-44}+{1,1,2,3,5,7,9}
1019:n={0-44}+{1,2,3,4,5,6,8}
1020:n={0-44}+{1,2,3,4,5,6,9}
1021:n={0-44}+{1,2,3,4,5,7,9}
1022:n={0-44}+{1,1,2,3,4,5,7,9}
1023:n={0-44}+{1,1,2,3,4,5,7,10}
Prove by list failed for n=43
Search for 43 elements
1024:n={0-44}+{1,1,2,3,4,6,7,10}
1025:n={0-44}+{1,1,2,3,4,6,8,10}
1026:n={0-44}+{1,1,2,3,4,6,8,11}
1027:n={0-44}+{1,1,2,3,5,6,8,11}
1028:n={0-44}+{1,1,2,2,3,4,6,8,11}
1029:n={0-44}+{1,2,3,4,5,6,8,10}
1030:n={0-44}+{1,1,2,3,4,5,6,8,10}
1031:n={0-44}+{1,1,2,3,4,5,6,8,11}
1032:n={0-44}+{1,1,2,3,4,5,7,8,11}
1033:n={0-44}+{1,1,2,3,4,5,7,9,11}
1034:n={0-44}+{1,1,2,3,4,5,7,9,12}
Prove by list failed for n=44
Search for 44 elements
1035:n={0-44}+{}
1036:n={0-45}+{1}
1037:n={0-45}+{2}
1038:n={0-45}+{1,2}
1039:n={0-45}+{1,3}
1040:n={0-45}+{1,1,3}
1041:n={0-45}+{1,2,3}
1042:n={0-45}+{1,2,4}
1043:n={0-45}+{1,1,2,4}
1044:n={0-45}+{1,1,3,4}
1045:n={0-45}+{1,2,3,4}
1046:n={0-45}+{1,2,3,5}
1047:n={0-45}+{1,1,2,3,5}
1048:n={0-45}+{1,1,2,3,6}
1049:n={0-45}+{1,1,2,4,6}
1050:n={0-45}+{1,2,3,4,5}
1051:n={0-45}+{1,2,3,4,6}
1052:n={0-45}+{1,1,2,3,4,6}
1053:n={0-45}+{1,1,2,3,4,7}
1054:n={0-45}+{1,1,2,3,5,7}
1055:n={0-45}+{1,1,2,3,5,8}
1056:n={0-45}+{1,2,2,4,5,7}
1057:n={0-45}+{1,2,3,4,5,7}
1058:n={0-45}+{1,1,2,3,4,5,7}
1059:n={0-45}+{1,2,3,4,6,8}
1060:n={0-45}+{1,1,2,3,4,6,8}
1061:n={0-45}+{1,1,2,3,4,6,9}
1062:n={0-45}+{1,1,2,3,5,6,9}
1063:n={0-45}+{1,1,2,3,5,7,9}
1064:n={0-45}+{1,2,3,4,5,6,8}
1065:n={0-45}+{1,2,3,4,5,6,9}
1066:n={0-45}+{1,2,3,4,5,7,9}
1067:n={0-45}+{1,1,2,3,4,5,7,9}
Prove by list failed for n=44
Search for 44 elements
1068:n={0-45}+{1,1,2,3,4,5,7,10}
1069:n={0-45}+{1,1,2,3,4,6,7,10}
1070:n={0-45}+{1,1,2,3,4,6,8,10}
1071:n={0-45}+{1,1,2,3,4,6,8,11}
1072:n={0-45}+{1,1,2,3,5,6,8,11}
1073:n={0-45}+{1,1,2,2,3,4,6,8,11}
1074:n={0-45}+{1,2,3,4,5,6,8,10}
1075:n={0-45}+{1,1,2,3,4,5,6,8,10}
1076:n={0-45}+{1,1,2,3,4,5,6,8,11}
1077:n={0-45}+{1,1,2,3,4,5,7,8,11}
1078:n={0-45}+{1,1,2,3,4,5,7,9,11}
1079:n={0-45}+{1,1,2,3,4,5,7,9,12}
1080:n={0-45}+{1,1,2,3,4,6,7,9,12}
1081:n={0-45}+{}
1082:n={0-46}+{1}
1083:n={0-46}+{2}
1084:n={0-46}+{1,2}
1085:n={0-46}+{1,3}
1086:n={0-46}+{1,1,3}
1087:n={0-46}+{1,2,3}
1088:n={0-46}+{1,2,4}
1089:n={0-46}+{1,1,2,4}
1090:n={0-46}+{1,1,3,4}
1091:n={0-46}+{1,2,3,4}
1092:n={0-46}+{1,2,3,5}
1093:n={0-46}+{1,1,2,3,5}
1094:n={0-46}+{1,1,2,3,6}
1095:n={0-46}+{1,1,2,4,6}
1096:n={0-46}+{1,2,3,4,5}
1097:n={0-46}+{1,2,3,4,6}
1098:n={0-46}+{1,1,2,3,4,6}
1099:n={0-46}+{1,1,2,3,4,7}
1100:n={0-46}+{1,1,2,3,5,7}
1101:n={0-46}+{1,1,2,3,5,8}
1102:n={0-46}+{1,2,2,4,5,7}
1103:n={0-46}+{1,2,3,4,5,7}
1104:n={0-46}+{1,1,2,3,4,5,7}
1105:n={0-46}+{1,2,3,4,6,8}
1106:n={0-46}+{1,1,2,3,4,6,8}
1107:n={0-46}+{1,1,2,3,4,6,9}
1108:n={0-46}+{1,1,2,3,5,6,9}
1109:n={0-46}+{1,1,2,3,5,7,9}
1110:n={0-46}+{1,2,3,4,5,6,8}
1111:n={0-46}+{1,2,3,4,5,6,9}
1112:n={0-46}+{1,2,3,4,5,7,9}
Prove by list failed for n=45
Search for 45 elements
1113:n={0-46}+{1,1,2,3,4,5,7,9}
1114:n={0-46}+{1,1,2,3,4,5,7,10}
1115:n={0-46}+{1,1,2,3,4,6,7,10}
1116:n={0-46}+{1,1,2,3,4,6,8,10}
1117:n={0-46}+{1,1,2,3,4,6,8,11}
1118:n={0-46}+{1,2,2,3,4,6,8,11}
1119:n={0-46}+{1,1,2,2,3,4,6,8,11}
1120:n={0-46}+{1,2,3,4,5,6,8,10}
1121:n={0-46}+{1,1,2,3,4,5,6,8,10}
1122:n={0-46}+{1,1,2,3,4,5,6,8,11}
1123:n={0-46}+{1,1,2,3,4,5,7,8,11}
1124:n={0-46}+{1,1,2,3,4,5,7,9,11}
1125:n={0-46}+{1,1,2,3,4,5,7,9,12}
Prove by list failed for n=45
Search for 45 elements
1126:n={0-46}+{1,1,2,3,4,6,7,9,12}
1127:n={0-46}+{1,1,2,2,3,4,5,7,9,12}
1128:n={0-46}+{}
1129:n={0-47}+{1}
1130:n={0-47}+{2}
1131:n={0-47}+{1,2}
1132:n={0-47}+{1,3}
1133:n={0-47}+{1,1,3}
1134:n={0-47}+{1,2,3}
1135:n={0-47}+{1,2,4}
1136:n={0-47}+{1,1,2,4}
1137:n={0-47}+{1,1,3,4}
1138:n={0-47}+{1,2,3,4}
1139:n={0-47}+{1,2,3,5}
1140:n={0-47}+{1,1,2,3,5}
1141:n={0-47}+{1,1,2,3,6}
1142:n={0-47}+{1,1,2,4,6}
1143:n={0-47}+{1,2,3,4,5}
1144:n={0-47}+{1,2,3,4,6}
1145:n={0-47}+{1,1,2,3,4,6}
1146:n={0-47}+{1,1,2,3,4,7}
1147:n={0-47}+{1,1,2,3,5,7}
1148:n={0-47}+{1,1,2,3,5,8}
1149:n={0-47}+{1,2,2,4,5,7}
1150:n={0-47}+{1,2,3,4,5,7}
1151:n={0-47}+{1,1,2,3,4,5,7}
1152:n={0-47}+{1,1,2,3,4,5,8}
1153:n={0-47}+{1,1,2,3,4,6,8}
1154:n={0-47}+{1,1,2,3,4,6,9}
1155:n={0-47}+{1,1,2,3,5,6,9}
1156:n={0-47}+{1,1,2,3,5,7,9}
1157:n={0-47}+{1,2,3,4,5,6,8}
1158:n={0-47}+{1,2,3,4,5,6,9}
Prove by list failed for n=46
Search for 46 elements
1159:n={0-47}+{1,2,3,4,5,7,9}
1160:n={0-47}+{1,1,2,3,4,5,7,9}
1161:n={0-47}+{1,1,2,3,4,5,7,10}
1162:n={0-47}+{1,1,2,3,4,6,7,10}
1163:n={0-47}+{1,1,2,3,4,6,8,10}
1164:n={0-47}+{1,1,2,3,4,6,8,11}
1165:n={0-47}+{1,2,2,3,4,6,8,11}
1166:n={0-47}+{1,1,2,2,3,4,6,8,11}
1167:n={0-47}+{1,2,3,4,5,6,8,10}
1168:n={0-47}+{1,1,2,3,4,5,6,8,10}
1169:n={0-47}+{1,1,2,3,4,5,6,8,11}
1170:n={0-47}+{1,1,2,3,4,5,7,8,11}
1171:n={0-47}+{1,1,2,3,4,5,7,9,11}
Prove by list failed for n=46
Search for 46 elements
1172:n={0-47}+{1,1,2,3,4,5,7,9,12}
1173:n={0-47}+{1,1,2,3,4,6,7,9,12}
1174:n={0-47}+{1,1,2,2,3,4,5,7,9,12}
1175:n={0-47}+{1,1,2,2,3,4,6,7,9,12}
1176:n={0-47}+{}
1177:n={0-48}+{1}
1178:n={0-48}+{2}
1179:n={0-48}+{1,2}
1180:n={0-48}+{1,3}
1181:n={0-48}+{1,1,3}
1182:n={0-48}+{1,2,3}
1183:n={0-48}+{1,2,4}
1184:n={0-48}+{1,1,2,4}
1185:n={0-48}+{1,1,3,4}
1186:n={0-48}+{1,2,3,4}
1187:n={0-48}+{1,2,3,5}
1188:n={0-48}+{1,1,2,3,5}
1189:n={0-48}+{1,1,2,3,6}
1190:n={0-48}+{1,1,2,4,6}
1191:n={0-48}+{1,2,3,4,5}
1192:n={0-48}+{1,2,3,4,6}
1193:n={0-48}+{1,1,2,3,4,6}
1194:n={0-48}+{1,1,2,3,4,7}
1195:n={0-48}+{1,1,2,3,5,7}
1196:n={0-48}+{1,1,2,3,5,8}
1197:n={0-48}+{1,2,2,4,5,7}
1198:n={0-48}+{1,2,3,4,5,7}
1199:n={0-48}+{1,1,2,3,4,5,7}
1200:n={0-48}+{1,1,2,3,4,5,8}
1201:n={0-48}+{1,1,2,3,4,6,8}
1202:n={0-48}+{1,1,2,3,4,6,9}
1203:n={0-48}+{1,1,2,3,5,6,9}
1204:n={0-48}+{1,1,2,3,5,7,9}
1205:n={0-48}+{1,2,3,4,5,6,8}
Prove by list failed for n=47
Search for 47 elements
1206:n={0-48}+{1,2,3,4,5,6,9}
1207:n={0-48}+{1,2,3,4,5,7,9}
1208:n={0-48}+{1,1,2,3,4,5,7,9}
1209:n={0-48}+{1,1,2,3,4,5,7,10}
1210:n={0-48}+{1,1,2,3,4,6,7,10}
1211:n={0-48}+{1,1,2,3,4,6,8,10}
1212:n={0-48}+{1,1,2,3,4,6,8,11}
1213:n={0-48}+{1,2,2,3,4,6,8,11}
1214:n={0-48}+{1,1,2,2,3,4,6,8,11}
1215:n={0-48}+{1,2,3,4,5,6,8,10}
1216:n={0-48}+{1,1,2,3,4,5,6,8,10}
1217:n={0-48}+{1,1,2,3,4,5,6,8,11}
1218:n={0-48}+{1,1,2,3,4,5,7,8,11}
Prove by list failed for n=47
Search for 47 elements
1219:n={0-48}+{1,1,2,3,4,5,7,9,11}
1220:n={0-48}+{1,1,2,3,4,5,7,9,12}
1221:n={0-48}+{1,1,2,3,4,6,7,9,12}
1222:n={0-48}+{1,1,2,2,3,4,5,7,9,12}
1223:n={0-48}+{1,1,2,2,3,4,6,7,9,12}
1224:n={0-48}+{1,1,2,3,4,6,8,10,13}
1225:n={0-48}+{}
1226:n={0-49}+{1}
1227:n={0-49}+{2}
1228:n={0-49}+{1,2}
1229:n={0-49}+{1,3}
1230:n={0-49}+{1,1,3}
1231:n={0-49}+{1,2,3}
1232:n={0-49}+{1,2,4}
1233:n={0-49}+{1,1,2,4}
1234:n={0-49}+{1,1,3,4}
1235:n={0-49}+{1,2,3,4}
1236:n={0-49}+{1,2,3,5}
1237:n={0-49}+{1,1,2,3,5}
1238:n={0-49}+{1,1,2,3,6}
1239:n={0-49}+{1,1,2,4,6}
1240:n={0-49}+{1,2,3,4,5}
1241:n={0-49}+{1,2,3,4,6}
1242:n={0-49}+{1,1,2,3,4,6}
1243:n={0-49}+{1,1,2,3,4,7}
1244:n={0-49}+{1,1,2,3,5,7}
1245:n={0-49}+{1,1,2,3,5,8}
1246:n={0-49}+{1,2,2,4,5,7}
1247:n={0-49}+{1,2,3,4,5,7}
1248:n={0-49}+{1,1,2,3,4,5,7}
1249:n={0-49}+{1,1,2,3,4,5,8}
1250:n={0-49}+{1,1,2,3,4,6,8}
1251:n={0-49}+{1,1,2,3,4,6,9}
1252:n={0-49}+{1,1,2,3,5,6,9}
1253:n={0-49}+{1,1,2,3,5,7,9}
Prove by list failed for n=48
Search for 48 elements
1254:n={0-49}+{1,2,3,4,5,6,8}
1255:n={0-49}+{1,2,3,4,5,6,9}
1256:n={0-49}+{1,2,3,4,5,7,9}
1257:n={0-49}+{1,1,2,3,4,5,7,9}
1258:n={0-49}+{1,1,2,3,4,5,7,10}
1259:n={0-49}+{1,1,2,3,4,6,7,10}
1260:n={0-49}+{1,1,2,3,4,6,8,10}
1261:n={0-49}+{1,1,2,3,4,6,8,11}
1262:n={0-49}+{1,1,2,2,3,4,6,8,10}
1263:n={0-49}+{1,1,2,2,3,4,6,8,11}
1264:n={0-49}+{1,2,3,4,5,6,8,10}
1265:n={0-49}+{1,1,2,3,4,5,6,8,10}
1266:n={0-49}+{1,1,2,3,4,5,6,8,11}
Prove by list failed for n=48
Search for 48 elements
1267:n={0-49}+{1,1,2,3,4,5,7,8,11}
1268:n={0-49}+{1,1,2,3,4,5,7,9,11}
1269:n={0-49}+{1,1,2,3,4,5,7,9,12}
1270:n={0-49}+{1,1,2,3,4,6,7,9,12}
1271:n={0-49}+{1,1,2,2,3,4,5,7,9,12}
1272:n={0-49}+{1,1,2,2,3,4,6,7,9,12}
1273:n={0-49}+{1,1,2,2,3,4,6,7,9,13}
1274:n={0-49}+{1,1,2,3,4,5,6,7,9,11}
1275:n={0-49}+{}
1276:n={0-50}+{1}
1277:n={0-50}+{2}
1278:n={0-50}+{1,2}
1279:n={0-50}+{1,3}
1280:n={0-50}+{1,1,3}
1281:n={0-50}+{1,2,3}
1282:n={0-50}+{1,2,4}
1283:n={0-50}+{1,1,2,4}
1284:n={0-50}+{1,1,3,4}
1285:n={0-50}+{1,2,3,4}
1286:n={0-50}+{1,2,3,5}
1287:n={0-50}+{1,1,2,3,5}
1288:n={0-50}+{1,1,2,3,6}
1289:n={0-50}+{1,1,2,4,6}
1290:n={0-50}+{1,2,3,4,5}
1291:n={0-50}+{1,2,3,4,6}
1292:n={0-50}+{1,1,2,3,4,6}
1293:n={0-50}+{1,1,2,3,4,7}
1294:n={0-50}+{1,1,2,3,5,7}
1295:n={0-50}+{1,1,2,3,5,8}
1296:n={0-50}+{1,2,2,4,5,7}
1297:n={0-50}+{1,2,3,4,5,7}
1298:n={0-50}+{1,1,2,3,4,5,7}
1299:n={0-50}+{1,1,2,3,4,5,8}
1300:n={0-50}+{1,1,2,3,4,6,8}
1301:n={0-50}+{1,1,2,3,4,6,9}
1302:n={0-50}+{1,1,2,3,5,6,9}
Prove by list failed for n=49
Search for 49 elements
1303:n={0-50}+{1,1,2,3,5,7,9}
1304:n={0-50}+{1,2,3,4,5,6,8}
1305:n={0-50}+{1,2,3,4,5,6,9}
1306:n={0-50}+{1,2,3,4,5,7,9}
1307:n={0-50}+{1,1,2,3,4,5,7,9}
1308:n={0-50}+{1,1,2,3,4,5,7,10}
1309:n={0-50}+{1,1,2,3,4,6,7,10}
1310:n={0-50}+{1,1,2,3,4,6,8,10}
1311:n={0-50}+{1,1,2,3,4,6,8,11}
1312:n={0-50}+{1,1,2,2,3,4,6,8,10}
1313:n={0-50}+{1,1,2,2,3,4,6,8,11}
1314:n={0-50}+{1,2,3,4,5,6,8,10}
1315:n={0-50}+{1,1,2,3,4,5,6,8,10}
Prove by list failed for n=49
Search for 49 elements
1316:n={0-50}+{1,1,2,3,4,5,6,8,11}
1317:n={0-50}+{1,1,2,3,4,5,7,8,11}
1318:n={0-50}+{1,1,2,3,4,5,7,9,11}
1319:n={0-50}+{1,1,2,3,4,5,7,9,12}
1320:n={0-50}+{1,1,2,3,4,6,7,9,12}
1321:n={0-50}+{1,1,2,2,3,4,5,7,9,12}
1322:n={0-50}+{1,1,2,2,3,4,6,7,9,12}
1323:n={0-50}+{1,1,2,2,3,4,6,7,9,13}
1324:n={0-50}+{1,1,2,3,4,5,6,7,9,11}
1325:n={0-50}+{1,1,2,3,4,5,6,7,9,12}
1326:n={0-50}+{}
1327:n={0-51}+{1}
1328:n={0-51}+{2}
1329:n={0-51}+{1,2}
1330:n={0-51}+{1,3}
1331:n={0-51}+{1,1,3}
1332:n={0-51}+{1,2,3}
1333:n={0-51}+{1,2,4}
1334:n={0-51}+{1,1,2,4}
1335:n={0-51}+{1,1,3,4}
1336:n={0-51}+{1,2,3,4}
1337:n={0-51}+{1,2,3,5}
1338:n={0-51}+{1,1,2,3,5}
1339:n={0-51}+{1,1,2,3,6}
1340:n={0-51}+{1,1,2,4,6}
1341:n={0-51}+{1,2,3,4,5}
1342:n={0-51}+{1,2,3,4,6}
1343:n={0-51}+{1,1,2,3,4,6}
1344:n={0-51}+{1,1,2,3,4,7}
1345:n={0-51}+{1,1,2,3,5,7}
1346:n={0-51}+{1,1,2,3,5,8}
1347:n={0-51}+{1,2,2,4,5,7}
1348:n={0-51}+{1,2,3,4,5,7}
1349:n={0-51}+{1,1,2,3,4,5,7}
1350:n={0-51}+{1,1,2,3,4,5,8}
1351:n={0-51}+{1,1,2,3,4,6,8}
1352:n={0-51}+{1,1,2,3,4,6,9}
1353:n={0-51}+{1,1,2,3,5,6,9}
1354:n={0-51}+{1,1,2,3,5,7,9}
1355:n={0-51}+{1,2,3,4,5,6,8}
1356:n={0-51}+{1,2,3,4,5,6,9}
1357:n={0-51}+{1,2,3,4,5,7,9}
1358:n={0-51}+{1,1,2,3,4,5,7,9}
1359:n={0-51}+{1,1,2,3,4,5,7,10}
1360:n={0-51}+{1,1,2,3,4,6,7,10}
1361:n={0-51}+{1,1,2,3,4,6,8,10}
1362:n={0-51}+{1,1,2,3,4,6,8,11}
1363:n={0-51}+{1,1,2,2,3,4,6,8,10}
1364:n={0-51}+{1,1,2,2,3,4,6,8,11}
1365:n={0-51}+{1,2,3,4,5,6,8,10}
Prove by list failed for n=50
Search for 50 elements
1366:n={0-51}+{1,1,2,3,4,5,6,8,10}
1367:n={0-51}+{1,1,2,3,4,5,6,8,11}
1368:n={0-51}+{1,1,2,3,4,5,7,8,11}
1369:n={0-51}+{1,1,2,3,4,5,7,9,11}
1370:n={0-51}+{1,1,2,3,4,5,7,9,12}
1371:n={0-51}+{1,1,2,3,4,6,7,9,12}
1372:n={0-51}+{1,1,2,2,3,4,5,7,9,12}
1373:n={0-51}+{1,1,2,2,3,4,6,7,9,12}
1374:n={0-51}+{1,1,2,2,3,4,6,7,9,13}
1375:n={0-51}+{1,1,2,3,4,5,6,7,9,11}
1376:n={0-51}+{1,1,2,3,4,5,6,7,9,12}
1377:n={0-51}+{1,1,2,3,4,5,6,8,9,12}
1378:n={0-51}+{}
1379:n={0-52}+{1}
1380:n={0-52}+{2}
1381:n={0-52}+{1,2}
1382:n={0-52}+{1,3}
1383:n={0-52}+{1,1,3}
1384:n={0-52}+{1,2,3}
1385:n={0-52}+{1,2,4}
1386:n={0-52}+{1,1,2,4}
1387:n={0-52}+{1,1,3,4}
1388:n={0-52}+{1,2,3,4}
1389:n={0-52}+{1,2,3,5}
1390:n={0-52}+{1,1,2,3,5}
1391:n={0-52}+{1,1,2,3,6}
1392:n={0-52}+{1,1,2,4,6}
1393:n={0-52}+{1,2,3,4,5}
1394:n={0-52}+{1,2,3,4,6}
1395:n={0-52}+{1,1,2,3,4,6}
1396:n={0-52}+{1,1,2,3,4,7}
1397:n={0-52}+{1,1,2,3,5,7}
1398:n={0-52}+{1,1,2,3,5,8}
1399:n={0-52}+{1,2,2,4,5,7}
1400:n={0-52}+{1,2,3,4,5,7}
1401:n={0-52}+{1,1,2,3,4,5,7}
1402:n={0-52}+{1,1,2,3,4,5,8}
1403:n={0-52}+{1,1,2,3,4,6,8}
1404:n={0-52}+{1,1,2,3,4,6,9}
1405:n={0-52}+{1,1,2,3,5,6,9}
1406:n={0-52}+{1,1,2,3,5,7,9}
1407:n={0-52}+{1,2,3,4,5,6,8}
1408:n={0-52}+{1,2,3,4,5,6,9}
1409:n={0-52}+{1,2,3,4,5,7,9}
1410:n={0-52}+{1,1,2,3,4,5,7,9}
1411:n={0-52}+{1,1,2,3,4,5,7,10}
1412:n={0-52}+{1,1,2,3,4,6,7,10}
1413:n={0-52}+{1,1,2,3,4,6,8,10}
1414:n={0-52}+{1,1,2,3,4,6,8,11}
1415:n={0-52}+{1,1,2,2,3,4,6,8,10}
1416:n={0-52}+{1,1,2,2,3,4,6,8,11}
Prove by list failed for n=51
Search for 51 elements
1417:n={0-52}+{1,2,3,4,5,6,8,10}
1418:n={0-52}+{1,1,2,3,4,5,6,8,10}
1419:n={0-52}+{1,1,2,3,4,5,6,8,11}
1420:n={0-52}+{1,1,2,3,4,5,7,8,11}
1421:n={0-52}+{1,1,2,3,4,5,7,9,11}
1422:n={0-52}+{1,1,2,3,4,5,7,9,12}
1423:n={0-52}+{1,1,2,3,4,6,7,9,12}
1424:n={0-52}+{1,1,2,2,3,4,5,7,9,12}
1425:n={0-52}+{1,1,2,2,3,4,6,7,9,12}
1426:n={0-52}+{1,1,2,2,3,4,6,7,9,13}
1427:n={0-52}+{1,1,2,3,4,5,6,7,9,11}
1428:n={0-52}+{1,1,2,3,4,5,6,7,9,12}
1429:n={0-52}+{1,1,2,3,4,5,6,8,9,12}
1430:n={0-52}+{1,1,2,3,4,5,6,8,10,12}
1431:n={0-52}+{}
1432:n={0-53}+{1}
1433:n={0-53}+{2}
1434:n={0-53}+{1,2}
1435:n={0-53}+{1,3}
1436:n={0-53}+{1,1,3}
1437:n={0-53}+{1,2,3}
1438:n={0-53}+{1,2,4}
1439:n={0-53}+{1,1,2,4}
1440:n={0-53}+{1,1,3,4}
1441:n={0-53}+{1,2,3,4}
1442:n={0-53}+{1,2,3,5}
1443:n={0-53}+{1,1,2,3,5}
1444:n={0-53}+{1,1,2,3,6}
1445:n={0-53}+{1,1,2,4,6}
1446:n={0-53}+{1,2,3,4,5}
1447:n={0-53}+{1,2,3,4,6}
1448:n={0-53}+{1,1,2,3,4,6}
1449:n={0-53}+{1,1,2,3,4,7}
1450:n={0-53}+{1,1,2,3,5,7}
1451:n={0-53}+{1,1,2,3,5,8}
1452:n={0-53}+{1,2,2,4,5,7}
1453:n={0-53}+{1,2,3,4,5,7}
1454:n={0-53}+{1,1,2,3,4,5,7}
1455:n={0-53}+{1,1,2,3,4,5,8}
1456:n={0-53}+{1,1,2,3,4,6,8}
1457:n={0-53}+{1,1,2,3,4,6,9}
1458:n={0-53}+{1,1,2,3,5,6,9}
1459:n={0-53}+{1,1,2,3,5,7,9}
1460:n={0-53}+{1,2,3,4,5,6,8}
1461:n={0-53}+{1,1,2,3,4,5,6,8}
1462:n={0-53}+{1,2,3,4,5,7,9}
1463:n={0-53}+{1,1,2,3,4,5,7,9}
1464:n={0-53}+{1,1,2,3,4,5,7,10}
1465:n={0-53}+{1,1,2,3,4,6,7,10}
1466:n={0-53}+{1,1,2,3,4,6,8,10}
1467:n={0-53}+{1,1,2,3,4,6,8,11}
1468:n={0-53}+{1,1,2,2,3,4,6,8,10}
Prove by list failed for n=52
Search for 52 elements
1469:n={0-53}+{1,1,2,2,3,4,6,8,11}
1470:n={0-53}+{1,2,3,4,5,6,8,10}
1471:n={0-53}+{1,1,2,3,4,5,6,8,10}
1472:n={0-53}+{1,1,2,3,4,5,6,8,11}
1473:n={0-53}+{1,1,2,3,4,5,7,8,11}
1474:n={0-53}+{1,1,2,3,4,5,7,9,11}
1475:n={0-53}+{1,1,2,3,4,5,7,9,12}
1476:n={0-53}+{1,2,2,3,4,5,7,9,12}
1477:n={0-53}+{1,1,2,2,3,4,5,7,9,12}
1478:n={0-53}+{1,1,2,2,3,4,6,7,9,12}
1479:n={0-53}+{1,1,2,2,3,4,6,7,9,13}
1480:n={0-53}+{1,1,2,3,4,5,6,7,9,11}
1481:n={0-53}+{1,1,2,3,4,5,6,7,9,12}
1482:n={0-53}+{1,1,2,3,4,5,6,8,9,12}
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。