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 A370830 Primes p such that the polynomial x^4-x^3-x^2-x-1 is irreducible mod p. 2

%I #29 Mar 22 2024 17:21:33

%S 2,5,31,43,53,79,83,89,97,109,131,139,151,199,229,233,239,283,313,317,

%T 359,367,389,433,443,479,487,569,571,577,601,617,641,643,659,677,769,

%U 797,823,853,857,929,937,941,971,1013,1019,1049,1063,1069,1087,1093,1117,1163,1171,1181,1231,1249,1283

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

%H Robert Israel, <a href="/A370830/b370830.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (Python)

%o from itertools import islice

%o from sympy import Poly, nextprime

%o from sympy.abc import x

%o def A370830_gen(): # generator of terms

%o p = 2

%o while True:

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

%o yield p

%o p = nextprime(p)

%o A370830_list = list(islice(A370830_gen(),20)) # _Chai Wah Wu_, Mar 14 2024

%Y Subsequence of A106283. Cf. 106309.

%K nonn

%O 1,1

%A _Robert Israel_, Mar 13 2024

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Last modified June 20 23:18 EDT 2024. Contains 373535 sequences. (Running on oeis4.)