%I #9 Jun 13 2017 23:51:35
%S 6,17,4,17,76,32,14,209,55,261,15,19,51,23,42,23,40,19,53,54,43,51,81,
%T 159,31,55,30,53,34,266,33,54,70,39,77,38,174,43,146,141,114,83,230,
%U 51,53,47,75,85,80,61,82,321,58,80,113,61,68,59,93,342,90,183,228,75,87,97
%N Least x satisfying n^3 + x^3 + y^3 = z^3, where (n,x,y,z),n<x<y<z forms a primitive quadruple.
%C There are a few small cases where the least x needs y>1000, e.g. 8^3+209^3+1744^3=1745^3. The S. Dutch link has a few nonprimitive quartets which have to be excluded for this sequence, e.g. 37^3+222^3+296^3=333^3. - _Martin Fuller_, Aug 11 2006
%H S. Dutch, <a href="http://www.uwgb.edu/dutchs/RECMATH/Cubesums.htm">Cubic Quartets With a,b,c<1000</a>
%o (PARI) A(n)=local(x,y,z);x=n+1;while(1,y=x+1;while(n^3+x^3+y^3>=(y+1)^3,if(ispower(n^3+x^3+y^3,3,&z) && (gcd([n,x,y,z])==1), return(x));y++;);x++;); \\ _Martin Fuller_, Aug 11 2006
%Y Cf. A120931, A120932.
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Jul 16 2006
%E Corrected by _R. J. Mathar_, Nov 25 2006
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