OFFSET
1,1
COMMENTS
The 2-class number of these fields is always 4.
Primes of the form 2x^2 - 2xy + 11y^2 with x nonnegative and y positive. - T. D. Noe, May 08 2005
Also primes of the forms 8x^2 + 4xy + 11y^2 and 11x^2 + 2xy + 23y^2. See A140633. - T. D. Noe, May 19 2008
The discriminant of positive definite binary quadratic form (2,2,11) is -84. - Hugo Pfoertner, Jul 14 2019
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
FORMULA
The primes are congruent to {2, 11, 23, 71} (mod 84). - T. D. Noe, May 02 2008
MATHEMATICA
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 *)
PROG
(Magma) [p: p in PrimesUpTo(3000) | p mod 84 in [2, 11, 23, 71]]; // Vincenzo Librandi, Jul 19 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 19 2005
STATUS
approved