A057751 Irreducible trinomials of prime degree for some k: x^p + x^k + 1 is irreducible over GF(2) for at least one k, p>k>0.

2, 3, 5, 7, 11, 17, 23, 29, 31, 41, 47, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 313, 337, 353, 359, 367, 383, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593, 599, 601

Offset

0,1

Links

Table of n, a(n) for n=0..55.

Example

The prime 79 is included because x^79 + x^9 + 1 is irreducible over GF(2). Only the primes 2 and 3 are irreducible for all ks between 0 and p. So far about one-half of all trinomials of a prime power are irreducible over GF(2) for at least one k between 0 and p.

Mathematica

Do[ k=1; While[ ToString[ Factor[ x^Prime[n ] + x^k + 1, Modulus ->2 ] ] != ToString[ x^Prime[n ] + x^k + 1 ] && k < Prime[n ], k++ ]; If[ k != Prime[ n ], Print[ Prime[ n ] ] ], {n, 1, 100} ]

Crossrefs

Sequence in context: A164641 A058982 A040069 * A040046 A075551 A070866

Adjacent sequences: A057748 A057749 A057750 * A057752 A057753 A057754

Keyword

nonn

Author

Robert G. Wilson v, Oct 30 2000

Status

approved