1,2

The sequence is finite by Thue's theorem

n(n + 1)(n + 2) + 1 = n^3 + 3*n^2 + 2*n + 1. The set of x values of integral solutions to the elliptic curve y^2 = n^3 + 3*n^2 + 2*n + 1 (see MAGMA program) is { -2, -1, 0, 2, 4, 55 }. So the sequence is complete. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 29 2007

(MAGMA) P<n> := PolynomialRing(Integers()); {x: x in Sort([ p[1] : p in IntegralPoints(EllipticCurve(n^3 + 3*n^2 + 2*n + 1)) ])}; - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 29 2007

Sequence in context: A018337 A092389 A005274 this_sequence A084574 A087621 A062784

Adjacent sequences: A121231 A121232 A121233 this_sequence A121235 A121236 A121237

fini,nonn,full

Roger Cuculiere (rcuculiere(AT)free.fr), Aug 21 2006