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 A254324 Least Y such that X^3 + Y^3 = A020898(n)*Z^3 for some X <= Y and some Z. 2

%I

%S 1,37,5,2,89,7,683

%N Least Y such that X^3 + Y^3 = A020898(n)*Z^3 for some X <= Y and some Z.

%C Also, max {X,Y,Z} for the smallest (in this sense of this sup norm) positive integer solution (X,Y,Z) to X^3 + Y^3 = A020898(n)*Z^3.

%C The X values are given in A254326.

%C a(8) > 10^5, with A020898(8)=17. Then the sequence continues a(9,10,...) = 5, 19, ?, 75, 3, 163, ?, 1853, ?, 3, 19, ...

%e A020898(1)=2 and 1^3 + 1^3 = 2*1^3, therefore a(1)=1.

%e A020898(2)=6 and 17^3 + 37^3 = 6*21^3, and there is no "smaller" solution (with X, Y, Z < 37), therefore a(2)=37.

%o (PARI) a(n,L=10^9)={n=if(n>0,A020898[n],-n); for(b=1,L,for(a=1,b,(a^3+b^3)%n&&next;ispower((a^3+b^3)/n,3)&&return(b)))}

%Y Cf. A020898, A254326.

%K nonn,more

%O 1,2

%A _M. F. Hasler_, Jan 27 2015

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)