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.

A132414 Integers n such that n^3 - (n + 2)^2 + n + 4 is a square.

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%I A132414 #15 Sep 08 2022 08:45:31
%S A132414 -1,0,3,4,75
%N A132414 Integers n such that n^3 - (n + 2)^2 + n + 4 is a square.
%C A132414 n^3 - (n + 2)^2 + n + 4 = n^3 - n^2 - 3*n. The set of x values of integral solutions to the elliptic curve y^2 = n^3 - n^2 - 3*n (see Magma program) is {-1, 0, 3, 4, 75}. - _Klaus Brockhaus_, Nov 13 2007
%e A132414 0^3 - 2^2 + 4 = 0^2, 3^3 - 5^2 + 7 = 3^2, 4^3 - 6^2 + 8 = 6^2 and 75^3 - 77^2 + 79 = 645^2.
%o A132414 (Magma) P<n> := PolynomialRing(Integers()); {x: x in Sort([ p[1] : p in IntegralPoints(EllipticCurve(n^3 - n^2 - 3*n)) ])}; /* _Klaus Brockhaus_, Nov 13 2007 */
%o A132414 (SageMath) [i[0] for i in EllipticCurve([0, -1, 0, -3, 0]).integral_points()] # _Seiichi Manyama_, Aug 26 2019
%Y A132414 Cf. A005563, A028560.
%K A132414 sign,fini,full
%O A132414 1,3
%A A132414 _Mohamed Bouhamida_, Nov 12 2007