A057460 Numbers k such that x^k + x^2 + 1 is irreducible over GF(2).

1, 3, 5, 11, 21, 29, 35, 93, 123, 333, 845, 4125, 10437, 10469, 14211, 20307, 34115, 47283, 50621, 57341, 70331, 80141

Offset

1,2

Comments

Any subsequent terms are > 300000. - Lucas A. Brown, Nov 28 2022

Links

Table of n, a(n) for n=1..22.

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.

Lucas A. Brown, Python program.

Lucas A. Brown, Sage program.

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)

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

a(21) and a(22) from Lucas A. Brown, Nov 28 2022

Status

approved