cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A347815 #24 Sep 16 2021 13:26:53
%S A347815 11,31,43,47,61,67,163,167,173,179,181,193,199,229,271,281,293,337,
%T A347815 349,383,401,439,449,457,491,503,547,569,641,647,659,661,673,677,773,
%U A347815 797,809,829,883,887,907,983,1013,1019,1021,1033,1039,1069,1223,1231
%N A347815 Prime numbers p such that both 30 and 105 are quadratic nonresidue (mod p).
%C A347815 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.
%C A347815 The sequence is infinite.
%H A347815 A. J. J. Heidrich, <a href="https://doi.org/10.1016/0022-314X(84)90050-7">On the factorization of Eulerian polynomials</a>, Journal of Number Theory, 18(2):157-168, 1984.
%t A347815 Select[Prime@Range[205], JacobiSymbol[30, #] == -1 && JacobiSymbol[105,#]==-1 &] (* _Stefano Spezia_, Sep 16 2021 *)
%o A347815 (PARI) isok(p) = isprime(p) && (kronecker(30, p)==-1) && (kronecker(105, p)==-1); \\ _Michel Marcus_, Sep 16 2021
%o A347815 (Python)
%o A347815 from sympy.ntheory import legendre_symbol, primerange
%o A347815 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
%Y A347815 Cf. A038904, A008292, A173018, A347816.
%K A347815 nonn
%O A347815 1,1
%A A347815 _Sela Fried_, Sep 15 2021