OFFSET
1,12
COMMENTS
Conventionally, no solution is indicated by (x,y) = (0,0).
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Mordell Curve
EXAMPLE
For n=12, the "min |x|" solution is 2^2 = (-2)^3+12, hence xy(12) = [-2,2] and a(12) = -2;
for n=18, it is 19^2 = 7^3 + 18, hence xy(18) = [7,19] and a(18) = 7.
MATHEMATICA
r[n_, x_] := Reduce[y >= 0 && y^2 == x^3 + n, y, Integers];
xy[n_] := If[A081119[[n]] == 0, {0, 0}, For[x = 0, True, x++, rn = r[n, x]; If[rn =!= False, Return[{x, y} /. ToRules[rn]]; Break[]]; rn = r[n, -x]; If[rn =!= False, Return[{-x, y} /. ToRules[rn]]; Break[]]]];
a[n_] := xy[n][[1]];
a /@ Range[120]
CROSSREFS
KEYWORD
sign
AUTHOR
Jean-François Alcover, Nov 24 2019
STATUS
approved