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A038877 Primes p such that 6 is not a square mod p.

%I A038877 #29 May 24 2022 02:15:30
%S A038877 7,11,13,17,31,37,41,59,61,79,83,89,103,107,109,113,127,131,137,151,
%T A038877 157,179,181,199,223,227,229,233,251,257,271,277,281,347,349,353,367,
%U A038877 373,397,401,419,421,439,443,449
%N A038877 Primes p such that 6 is not a square mod p.
%C A038877 Contribution from _Cino Hilliard_, Sep 06 2004: (Start)
%C A038877 Also primes p such that p divides 3^(p-1)/2 + 2^(p-1)/2.
%C A038877 Also primes p such that p divides 6^(p-1)/2 + 1.
%C A038877 Also primes p such that p divides 6^(p-1)/2 + 4^(p-1)/2. (End)
%C A038877 Inert rational primes in the field Q(sqrt(6)). - _Alonso del Arte_, Oct 14 2012
%C A038877 Primes congruent to 7, 11, 13, or 17 mod 24.
%H A038877 Vincenzo Librandi, <a href="/A038877/b038877.txt">Table of n, a(n) for n = 1..1000</a>
%H A038877 <a href="/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>
%F A038877 a(n) ~ 2n log n. - _Charles R Greathouse IV_, Oct 15 2012
%e A038877 17 is in the sequence because there is no solution to the equation x^2 - 6y = 17 in integers.
%e A038877 19 is NOT in the sequence because x^2 - 6y = 19 has solutions in integers, as does x^2 - 6y^2 = 19, e.g., x = 5, y = 1, and therefore (5 - sqrt(6))*(5 + sqrt(6)) = 19.
%t A038877 Select[Prime@Range[120], JacobiSymbol[6, #] == -1 &] (* _Vincenzo Librandi_, Sep 08 2012 *)
%o A038877 (PARI)
%o A038877 forprime(p=2,500,if(kronecker(6,p)==-1, print1(p,", ")));
%o A038877 /* _Joerg Arndt_, Oct 15 2012 */
%Y A038877 Cf. A003630.
%K A038877 nonn,easy
%O A038877 1,1
%A A038877 _N. J. A. Sloane_
%E A038877 Offset changed from 0 to 1 by _Vincenzo Librandi_, Sep 08 2012