A057484 Numbers n such that x^n + x^5 + x^4 + x^3 + x^2 + x + 1 is irreducible over GF(2).

1, 2, 3, 4, 5, 7, 8, 12, 14, 16, 17, 18, 19, 21, 23, 36, 37, 42, 61, 88, 112, 147, 171, 239, 253, 302, 304, 333, 402, 472, 597, 619, 718, 824, 1011, 1127, 1347, 1653, 1726, 1813, 3043, 3449, 4123, 4208, 5493, 7702, 8512, 10371, 13942, 14687, 20174, 22027, 24067, 25799, 28716, 29774, 31026, 31923, 33406, 34347, 42569, 52533, 54349

Offset

1,2

Links

Table of n, a(n) for n=1..63.

Prog

(SageMath)
P.<x> = GF(2)[]
for n in range(1, 10^5):
    p = (x^n + x^5 + x^4 + x^3 + x^2 + x + 1);
    if p.is_irreducible():
        print(n)
# Joerg Arndt, Apr 28 2012

Crossrefs

Sequence in context: A046098 A258085 A247350 * A091997 A124168 A379972

Adjacent sequences: A057481 A057482 A057483 * A057485 A057486 A057487

Keyword

nonn

Author

Robert G. Wilson v, Sep 27 2000

Extensions

Added terms 1, 2, 3, 4, 5 and terms >= 824, Joerg Arndt, Apr 28 2012

Status

approved