cp's OEIS Frontend

A102273 Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = -1, chi_{-7} = +1.

%I A102273 #27 Sep 08 2022 08:45:16
%S A102273 11,23,71,107,179,191,239,263,347,359,431,443,491,599,659,683,743,827,
%T A102273 863,911,947,1019,1031,1103,1163,1187,1283,1367,1439,1451,1499,1523,
%U A102273 1583,1607,1619,1667,1787,1871,2003,2027,2039,2087
%N A102273 Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = -1, chi_{-7} = +1.
%C A102273 The 2-class number of these fields is always 4.
%C A102273 Primes of the form 2x^2 - 2xy + 11y^2 with x nonnegative and y positive. - _T. D. Noe_, May 08 2005
%C A102273 Also primes of the forms 8x^2 + 4xy + 11y^2 and 11x^2 + 2xy + 23y^2. See A140633. - _T. D. Noe_, May 19 2008
%C A102273 The discriminant of positive definite binary quadratic form (2,2,11) is -84. - _Hugo Pfoertner_, Jul 14 2019
%H A102273 Vincenzo Librandi, <a href="/A102273/b102273.txt">Table of n, a(n) for n = 1..1000</a>
%H A102273 H. Cohn and J. C. Lagarias, <a href="http://dx.doi.org/10.1090/S0025-5718-1983-0717716-8">On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies</a>, Math. Comp. 41 (1983), 711-730.
%H A102273 N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%F A102273 The primes are congruent to {2, 11, 23, 71} (mod 84). - _T. D. Noe_, May 02 2008
%t A102273 f[x_,y_]:=2*x^2+2*x*y+11*y^2; lst={};Do[Do[p=f[x,y];If[PrimeQ[p],AppendTo[lst,p]],{y,-5!,6!}],{x,-5!,6!}];Take[Union[lst],5! ] (* _Vladimir Joseph Stephan Orlovsky_, Jul 06 2009 *)
%o A102273 (Magma) [p: p in PrimesUpTo(3000) | p mod 84 in [2, 11, 23, 71]]; // _Vincenzo Librandi_, Jul 19 2012
%Y A102273 Cf. A102269-A102275.
%Y A102273 Cf. A139827.
%K A102273 nonn
%O A102273 1,1
%A A102273 _N. J. A. Sloane_, Feb 19 2005