A057474 Numbers k such that x^k + x^5 + 1 is irreducible over GF(2).

2, 3, 6, 9, 12, 14, 17, 20, 23, 44, 47, 63, 84, 129, 236, 278, 279, 297, 300, 647, 726, 737, 2574, 2660, 4233, 4500, 8207, 11900, 16046, 21983, 23999, 24596, 24849, 84929, 130926, 156308, 160046, 185142, 270641

Offset: 1

Author

Robert G. Wilson v, Sep 27 2000

Keywords

• nonn
• hard
• more

Comments

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

Links

• Joerg Arndt, Matters Computational (The Fxtbook), section 40.9.3 "Irreducible trinomials of the form 1 + x^k + x^d", p.850
• Lucas A. Brown, Python program.
• Lucas A. Brown, Sage program.

Crossrefs

Cf. A002475.

Programs

Sage

P. = GF(2)[]
for n in range(10^4):
    if (x^n+x^5+1).is_irreducible():
        print(n) # Joerg Arndt, Apr 28 2012

Extensions

a(23)-a(34) by Joerg Arndt, Apr 28 2012

a(35)-a(38) by Manfred Scheucher, Aug 18 2015

a(39) from Lucas A. Brown, Nov 28 2022