cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A134104 Complete list of solutions to y^2 = x^3 + 297; sequence gives y values.

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%I A134104 #6 Sep 08 2022 08:45:32
%S A134104 9,17,18,19,45,199,333,50265,28748141
%N A134104 Complete list of solutions to y^2 = x^3 + 297; sequence gives y values.
%C A134104 For corresponding x values see A134105.
%e A134104 a(1)^2 = 9^2 = 81 = A134105(1)^3 + 297 = -216 + 297.
%e A134104 a(2)^2 = 17^2 = 289 = A134105(2)^3 + 297 = -8 + 297.
%e A134104 a(3)^2 = 18^2 = 324 = A134105(3)^3 + 297 = 27 + 297.
%e A134104 a(4)^2 = 19^2 = 361 = A134105(4)^3 + 297 = 64 + 297.
%e A134104 a(5)^2 = 45^2 = 2025 = A134105(5)^3 + 297 = 1728 + 297.
%e A134104 a(6)^2 = 199^2 = 39601 = A134105(6)^3 + 297 = 39304 + 297.
%e A134104 a(7)^2 = 333^2 = 110889 = A134105(7)^3 + 297 = 110592 + 297.
%e A134104 a(8)^2 = 50265^2 = 2526570225 = A134105(8)^3 + 297 = 2526569928 + 297.
%e A134104 a(9)^2 = 28748141^2 = 826455610955881 = A134105(9)^3 + 297 = 826455610955584 + 297.
%t A134104 sol[x_] := Solve[y > 0 && x^3 - y^2 == -297, y, Integers];
%t A134104 Reap[For[x = 1, x < 10^5, x++, sx = sol[x]; If[sx != {}, xy = {x, y} /. sx[[1]]; Print[xy]; Sow[xy]]; sx = sol[-x]; If[sx != {}, xy = {-x, y} /. sx[[1]]; Print[xy]; Sow[xy]]]][[2, 1]][[All, 2]] // Sort (* _Jean-François Alcover_, Feb 07 2020 *)
%o A134104 (Magma) Sort([ Abs(p[2]) : p in IntegralPoints(EllipticCurve([0, 297])) ]); /* adapted from A029727 */
%Y A134104 Cf. A134105, A134102, A134106, A029727, A134043, A134073.
%K A134104 nonn,fini,full
%O A134104 1,1
%A A134104 _Klaus Brockhaus_, Oct 08 2007