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A371566
Primes p such that x^5 - x^4 - x^3 - x^2 - x - 1 is irreducible (mod p).
3
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
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
KEYWORD
nonn
AUTHOR
Robert Israel, Mar 27 2024
STATUS
approved