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%I #6 Sep 08 2022 08:45:32
%S 7,11,25,38,133,8669
%N Complete list of solutions to y^2 = x^3 + 113; sequence gives y values.
%C For corresponding x values see A134043.
%e a(1)^2 = 7^2 = 49 = A134042(1)^3 + 113 = -64 + 113.
%e a(2)^2 = 11^2 = 121 = A134042(2)^3 + 113 = 8 + 113.
%e a(3)^2 = 25^2 = 625 = A134042(3)^3 + 113 = 512 + 113.
%e a(4)^2 = 38^2 = 1444 = A134042(4)^3 + 113 = 1331+ 113.
%e a(5)^2 = 133^2 = 17689 = A134042(5)^3 + 113 = 17576 + 113.
%e a(6)^2 = 8669^2 = 75151561 = A134042(6)^3 + 113 = 75151448 + 113.
%t (Program does not produce first two terms) a = {}; Do[k = n^2 - (Floor[n^(2/3)])^3; If[(k > 112) && (k < 113), AppendTo[a, n]], {n, 1, 100000}]; a
%o (Magma) Sort([ Abs(p[2]) : p in IntegralPoints(EllipticCurve([0, 113])) ]); /* adapted from A029727 */
%Y Cf. A134042, A029727, A080761.
%K nonn,fini,full
%O 1,1
%A _Artur Jasinski_, Oct 03 2007
%E Edited and corrected by _Klaus Brockhaus_, Oct 04 2007
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