A370830 - OEIS

A370830

Primes p such that the polynomial x^4-x^3-x^2-x-1 is irreducible mod p.

2, 5, 31, 43, 53, 79, 83, 89, 97, 109, 131, 139, 151, 199, 229, 233, 239, 283, 313, 317, 359, 367, 389, 433, 443, 479, 487, 569, 571, 577, 601, 617, 641, 643, 659, 677, 769, 797, 823, 853, 857, 929, 937, 941, 971, 1013, 1019, 1049, 1063, 1069, 1087, 1093, 1117, 1163, 1171, 1181, 1231, 1249, 1283

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OFFSET

1,1

LINKS

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

MAPLE

P:= x^4 - x^3 - x^2 - x - 1:

select(p -> Irreduc(P) mod p, [seq(ithprime(i), i=1..1000)]);

PROG

(Python)

from itertools import islice

from sympy import Poly, nextprime

from sympy.abc import x

def A370830_gen(): # generator of terms

p = 2

while True:

if Poly(x*(x*(x*(x-1)-1)-1)-1, x, modulus=p).is_irreducible:

yield p

p = nextprime(p)

A370830_list = list(islice(A370830_gen(), 20)) # Chai Wah Wu, Mar 14 2024

CROSSREFS

Subsequence of A106283. Cf. 106309.

Sequence in context: A059086 A363243 A215168 * A266478 A107389 A261750

Adjacent sequences: A370827 A370828 A370829 * A370831 A370832 A370833

KEYWORD

nonn

AUTHOR

Robert Israel, Mar 13 2024

STATUS

approved