login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A086797 Discriminant of the polynomial x^n - x - 1. 4
0, 5, -23, -283, 2869, 49781, -776887, -17600759, 370643273, 10387420489, -275311670611, -9201412118867, 293959006143997, 11414881932150269, -426781883555301359, -18884637964090410991, 808793517812627212561, 40173648337182874339601 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)