A057749 Prime degrees of absolutely reducible trinomials: primes p such that x^p + x^k + 1 is reducible over GF(2) for all k, p>k>0.

13, 19, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 131, 139, 149, 157, 163, 173, 179, 181, 197, 211, 227, 229, 251, 269, 277, 283, 293, 307, 311, 317, 331, 347, 349, 373, 379, 389, 397, 419, 421, 443, 461, 467, 491, 499, 509, 523, 541, 547, 557, 563, 571

Offset: 1

Author

Robert G. Wilson v, Oct 30 2000

Keywords

• nonn

Programs

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, 144} ]

PARI

lista(nn) = {forprime(p=2, nn, ok = 1; for (k=1, p-1, if (polisirreducible(Mod(1,2)*(x^p + x^k + 1)), ok = 0; break);); if (ok, print1(p, ", ")););}