【讨论】ProjEuler[49]:质数中的等差数列

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原问题来自：http://forum.simwe.com/viewthread.php?tid=911960&extra=page%3D1%26amp%3Bfilter%3Dtype%26amp%3Btypeid%3D508

The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.

What 12-digit number do you form by concatenating the three terms in this sequence?

1487, 4817, 8147这三个数有如下特征：都是素数；由相同的数位组成（1,4,7,8）；三者构成等差数列。
已知在四位数中仍然有一组与此类似的等差数列，试找出来这三个数，并且按照这三个数字大小递增的顺序写出这十二个位数来

我用matlab 来实现，本来已经答复过，但是还是觉得放在这里大家一起讨论，会好一些

1. function dd=ex092603
   
2. tic
   
3. b=3:-1:0;
   
4. a=primes(10^length(b)-1);
   
5. a=a(a>10^(length(b)-1));
   
6. [e,f,g]=unique(sort(mod(floor(bsxfun(@rdivide,repmat(a',1,length(b)),10.^b)),10),2),'rows');
   
7. pc=accumarray(g,a',[],@(x){x});
   
8. dd=cell2mat(cellfun(@isContinuePrimes,pc,'UniformOutput',false));
   
9. toc
   
10. function y=isContinuePrimes(x)
    
11. y=[];
    
12. if length(x)>2
    
13.     y0=nchoosek(x,3);
    
14.     y1=(max(y0,[],2)+min(y0,[],2))/2;
    
15.     y2=y1==mean(y0,2);
    
16.     if any(y2)
    
17.         y=y0(y2,:);
    
18.     end
    
19. end
    

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1. 
   
2. Elapsed time is 0.071698 seconds.
   
3. ans =
   
4.         1487        4817        8147
   
5.         6299        9629        2969
   

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