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

Author

Robert G. Wilson v, Sep 27 2000

Keywords

• nonn
• more

Comments

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

Links

• 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)

Crossrefs

Cf. A002475, A074710.

Programs

PARI

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

Extensions

Confirmed by Richard P. Brent, Sep 05 2002

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