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%I #3 Mar 30 2012 17:27:41
%S 10,13,12,56,48,40,49,23,29,47,45,46,70,69,70,79,40,34,92,117,56,128,
%T 102,176,38,160,19,98,125,16,20,79,110,56,130,70,90,77,124,15,65,90,
%U 124,195,270,65,205,23,35,209,78,58,237,33,70,304,91,286,176,274,238,238,28
%N First component of quadruples a,b,c,d such that a < b < c < d, (a*b*c) mod (a+b+c) = d, (a*b*d) mod (a+b+d) = c, (a*c*d) mod (a+c+d) = b, (b*c*d) mod (b+c+d) = a. The quadruples are ordered according to sum of first three components, secondary by first component, thirdly by second component.
%C Suggested by Thomas A. Nagy. - A092888 gives second component, A092889 gives third component, A092890 gives fourth component.
%C Problem: Which numbers will never appear as one of the components of those quadruples?
%e The sixth quadruple is 40, 70, 142, 196, hence a(6) = 40.
%o (PARI) {m=1320;for(n=6,m, for(a=1,(n-3)\3, for(b=a+1,(n-a-1)\2,c=n-a-b;d=a*b*c%(a+b+c); if(c<d,if(a*b*d%(a+b+d)==c,if(a*c*d%(a+c+d)==b,if(b*c*d%(b+c+d)==a,print1(a,","))))))))}
%Y Cf. A092888, A092889, A092890, A092891.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Mar 12 2004
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