A057476 Numbers k such that x^k + x^6 + 1 is irreducible over GF(2).

1, 3, 5, 7, 17, 31, 71, 97, 167, 175, 209, 385, 2159, 5617, 8921, 33425, 39119, 76625, 110249, 192127, 255265

Offset: 1

Author

Robert G. Wilson v, Sep 27 2000

Keywords

• nonn
• more

Comments

a(16) > 30000 if it exists. - Robert Israel, Nov 11 2016

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

Links

• Lucas A. Brown, Python program.
• Lucas A. Brown, Sage program.

Crossrefs

Cf. A002475.

Programs

Maple

select(n -> Irreduc(x^n+x^6+1) mod 2, [$1..1000]); # Robert Israel, Nov 11 2016

Extensions

a(13)-a(15) from Robert Israel, Nov 11 2016

a(16)-a(21) from Lucas A. Brown, Nov 28 2022