A371566 Primes p such that x^5 - x^4 - x^3 - x^2 - x - 1 is irreducible (mod p).

5, 7, 11, 13, 17, 31, 37, 41, 53, 79, 107, 199, 233, 239, 311, 331, 337, 389, 463, 523, 541, 547, 557, 563, 577, 677, 769, 853, 937, 971, 1009, 1021, 1033, 1049, 1061, 1201, 1237, 1291, 1307, 1361, 1427, 1453, 1543, 1657, 1699, 1723, 1747, 1753, 1759, 1787, 1801, 1811, 1861, 1877, 1997, 1999

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

P:= x^5 - x^4 - x^3 - x^2 - x - 1:
select(p -> Irreduc(P) mod p, [seq(ithprime(i), i=1..1000)]); # Robert Israel, Mar 13 2024

Mathematica

P = x^5 - x^4 - x^3 - x^2 - x - 1;
Select[Prime[Range[1000]], IrreduciblePolynomialQ[P, Modulus -> #]&] (* Jean-François Alcover, Mar 24 2024, after Robert Israel *)

Prog

(Python)
from itertools import islice
from sympy import Poly, nextprime
from sympy.abc import x
def A371566_gen(): # generator of terms
    p = 2
    while True:
        if Poly(x*(x*(x*(x*(x-1)-1)-1)-1)-1, x, modulus=p).is_irreducible:
            yield p
        p = nextprime(p)
A371566_list = list(islice(A371566_gen(), 20)) # Chai Wah Wu, Mar 14 2024
(PARI) a371566(upto) = forprime (p=2, upto, my(f=factormod(x^5 - x^4 - x^3 - x^2 - x - 1, p)); if(#f[, 1]==1, print1(p, ", "))) \\ Hugo Pfoertner, Mar 22 2024

Crossrefs

Contained in, but not equal to, A106309. Cf. A370830.

Sequence in context: A109416 A132170 A106309 * A227576 A114262 A255229

Adjacent sequences: A371563 A371564 A371565 * A371567 A371568 A371569

Keyword

nonn

Author

Robert Israel, Mar 27 2024

Status

approved