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

1,1

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

Table of n, a(n) for n=1..50.

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A038904, A008292, A173018, A347816.

Sequence in context: A144234 A109548 A173767 * A142343 A271653 A043124

Adjacent sequences: A347812 A347813 A347814 * A347816 A347817 A347818

Keyword

nonn

Author

Sela Fried, Sep 15 2021

Status

approved