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A191059 Primes p that have Kronecker symbol (p|6) = -1.

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%I A191059 #31 Oct 23 2024 20:27:17
%S A191059 13,17,19,23,37,41,43,47,61,67,71,89,109,113,137,139,157,163,167,181,
%T A191059 191,211,229,233,239,257,263,277,281,283,307,311,331,349,353,359,373,
%U A191059 379,383,397,401,421,431,449,479,499,503,521,523,541,547,569,571,593
%N A191059 Primes p that have Kronecker symbol (p|6) = -1.
%C A191059 Inert rational primes in the field Q(sqrt(-6)). - _N. J. A. Sloane_, Dec 26 2017
%C A191059 Appears to be the primes p such that (p mod 6)*(Fibonacci(p) mod 6) = 5. - _Gary Detlefs_, May 26 2014
%C A191059 Originally erroneously named "Primes that are not squares mod 6". - _M. F. Hasler_, Jan 18 2016
%C A191059 From _Jianing Song_, Oct 23 2024: (Start)
%C A191059 Primes p such that the Legendre symbol (-6/p) = -1, i.e., -6 is not a square modulo p.
%C A191059 Primes congruent to {13, 17, 19, 23} module 24. (End)
%H A191059 Vincenzo Librandi, <a href="/A191059/b191059.txt">Table of n, a(n) for n = 1..1000</a>
%H A191059 <a href="https://oeis.org/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>
%t A191059 Select[Prime[Range[200]], JacobiSymbol[#,6]==-1&]
%o A191059 (Magma) [p: p in PrimesUpTo(593) | KroneckerSymbol(p, 6) eq -1]; // _Vincenzo Librandi_, Sep 11 2012
%o A191059 (PARI) is(n)=isprime(n) && kronecker(n,6)<0 \\ _Charles R Greathouse IV_, Feb 23 2017
%Y A191059 Cf. A157437.
%K A191059 nonn,easy
%O A191059 1,1
%A A191059 _T. D. Noe_, May 25 2011
%E A191059 Definition corrected, following a suggestion from _David Broadhurst_, by _M. F. Hasler_, Jan 18 2016