A086797 Discriminant of the polynomial x^n - x - 1.

0, 5, -23, -283, 2869, 49781, -776887, -17600759, 370643273, 10387420489, -275311670611, -9201412118867, 293959006143997, 11414881932150269, -426781883555301359, -18884637964090410991, 808793517812627212561, 40173648337182874339601

Offset

1,2

Comments

Selmer proved that for all n the Galois group of the polynomial x^n - x - 1 over the rationals is the symmetric group S_n. [Comment corrected by Artur Jasinski, Feb 06 2007]

Links

Table of n, a(n) for n=1..18.

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.

H. Osada, The Galois groups of the polynomials X^n + a X^l + b, Journal of Number Theory, Feb. 1987, vol. 25, (no.2):230-8.

Ernst S. Selmer, On the irreducibility of certain trinomials, Math. Scand., 4 (1956) 287-302.

Formula

Except for the sign, the sequence alternates between the sum and difference of consecutive terms of A000312. a(n) = (n^n + (-1)^n (n-1)^(n-1))*(-1)^ceiling(1+n/2). - T. D. Noe, Aug 13 2004

Prog

(PARI) a(n)=poldisc(x^n-x-1)

Crossrefs

Cf. A000312 (n^n), A007781 (n^n - (n-1)^(n-1)), A056788 (n^n + (n-1)^(n-1)).

Cf. A086783.

Sequence in context: A197936 A198029 A072104 * A023275 A018899 A080990

Adjacent sequences: A086794 A086795 A086796 * A086798 A086799 A086800

Keyword

sign

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 05 2003

Extensions

More terms from Benoit Cloitre, Aug 06 2003

Status

approved