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Primes p that have Kronecker symbol (p|6) = -1.
4

%I #31 Oct 23 2024 20:27:17

%S 13,17,19,23,37,41,43,47,61,67,71,89,109,113,137,139,157,163,167,181,

%T 191,211,229,233,239,257,263,277,281,283,307,311,331,349,353,359,373,

%U 379,383,397,401,421,431,449,479,499,503,521,523,541,547,569,571,593

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

%C Inert rational primes in the field Q(sqrt(-6)). - _N. J. A. Sloane_, Dec 26 2017

%C Appears to be the primes p such that (p mod 6)*(Fibonacci(p) mod 6) = 5. - _Gary Detlefs_, May 26 2014

%C Originally erroneously named "Primes that are not squares mod 6". - _M. F. Hasler_, Jan 18 2016

%C From _Jianing Song_, Oct 23 2024: (Start)

%C Primes p such that the Legendre symbol (-6/p) = -1, i.e., -6 is not a square modulo p.

%C Primes congruent to {13, 17, 19, 23} module 24. (End)

%H Vincenzo Librandi, <a href="/A191059/b191059.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="https://oeis.org/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>

%t Select[Prime[Range[200]], JacobiSymbol[#,6]==-1&]

%o (Magma) [p: p in PrimesUpTo(593) | KroneckerSymbol(p, 6) eq -1]; // _Vincenzo Librandi_, Sep 11 2012

%o (PARI) is(n)=isprime(n) && kronecker(n,6)<0 \\ _Charles R Greathouse IV_, Feb 23 2017

%Y Cf. A157437.

%K nonn,easy,changed

%O 1,1

%A _T. D. Noe_, May 25 2011

%E Definition corrected, following a suggestion from _David Broadhurst_, by _M. F. Hasler_, Jan 18 2016