login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057460 Numbers n such that x^n + x^2 + 1 is irreducible over GF(2). 3
1, 3, 5, 11, 21, 29, 35, 93, 123, 333, 845, 4125, 10437, 10469, 14211, 20307, 34115, 47283, 50621, 57341 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

Joerg Arndt, Matters Computational (The Fxtbook)

I. F. Blake, S. Gao and R. J. Lambert, Constructive problems for irreducible polynomials over finite fields, in Information Theory and Applications, LNCS 793, Springer-Verlag, Berlin, 1994, 1-23, See Table 2.

H. Fredricksen, R. Wisniewski, On trinomials x^n + x^2 + 1 and x^{8l+-1} + x^k + 1 irreducible overGF(2), Inform. and Control 50 (1981), no. 1, 58--63. MR0665139 (84i:12013). Gives first 20 terms.

Index entries for sequences related to trinomials over GF(2)

MATHEMATICA

Do[ If[ ToString[ Factor[ x^n + x^2 + 1, Modulus -> 2 ] ] == ToString[ x^n + x^2 + 1 ], Print[ n ] ], {n, 0, 750} ]

PROG

(PARI) isok(n) = polisirreducible(Mod(1, 2)*(x^n + x^2 + 1)); \\ Michel Marcus, Aug 23 2015

CROSSREFS

Cf. A002475, A074710.

Sequence in context: A281318 A082713 A074710 * A269112 A093328 A045515

Adjacent sequences:  A057457 A057458 A057459 * A057461 A057462 A057463

KEYWORD

nonn,more

AUTHOR

Robert G. Wilson v, Sep 27 2000

EXTENSIONS

Confirmed by Richard P. Brent, Sep 05 2002

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 February 24 16:26 EST 2020. Contains 332209 sequences. (Running on oeis4.)