A347815 Prime numbers p such that both 30 and 105 are quadratic nonresidue (mod p).

11, 31, 43, 47, 61, 67, 163, 167, 173, 179, 181, 193, 199, 229, 271, 281, 293, 337, 349, 383, 401, 439, 449, 457, 491, 503, 547, 569, 641, 647, 659, 661, 673, 677, 773, 797, 809, 829, 883, 887, 907, 983, 1013, 1019, 1021, 1033, 1039, 1069, 1223, 1231

Offset: 1

Author

Sela Fried, Sep 15 2021

Keywords

• nonn

Comments

Primes p such that the Eulerian polynomial E_5(x) is irreducible (mod p), where E_5(x) = x^4 + 26x^3 + 66x^2 + 26x + 1.

The sequence is infinite.

Links

• A. J. J. Heidrich, On the factorization of Eulerian polynomials, Journal of Number Theory, 18(2):157-168, 1984.

Crossrefs

Cf. A038904, A008292, A173018, A347816.

Programs

Mathematica

Select[Prime@Range[205], JacobiSymbol[30, #] == -1 && JacobiSymbol[105,#]==-1 &] (* Stefano Spezia, Sep 16 2021 *)

PARI

isok(p) = isprime(p) && (kronecker(30, p)==-1) && (kronecker(105, p)==-1); \\ Michel Marcus, Sep 16 2021

Python

from sympy.ntheory import legendre_symbol, primerange
A347815_list = [p for p in primerange(3,10**5) if legendre_symbol(30,p) == legendre_symbol(105,p) == -1] # Chai Wah Wu, Sep 16 2021