

A132414


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


3




OFFSET

1,3


COMMENTS

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


LINKS

Table of n, a(n) for n=1..5.


EXAMPLE

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.


PROG

(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 */


CROSSREFS

Cf. A005563, A028560.
Sequence in context: A052323 A012087 A012194 * A041171 A279935 A111799
Adjacent sequences: A132411 A132412 A132413 * A132415 A132416 A132417


KEYWORD

sign,fini,full


AUTHOR

Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 12 2007


STATUS

approved



