A102271 Primes of the form 3x^2 + 7y^2.

3, 7, 19, 31, 103, 139, 199, 223, 271, 283, 307, 367, 439, 523, 607, 619, 643, 691, 727, 787, 811, 859, 1039, 1063, 1123, 1231, 1279, 1291, 1399, 1447, 1459, 1483, 1531, 1543, 1567, 1627, 1699, 1783, 1867, 1879, 1951, 1987, 2131, 2203, 2239

Offset

1,1

Comments

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

Links

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]

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 {3, 7, 19, 31, 55} (mod 84). - T. D. Noe, May 02 2008

Mathematica

m=3; n=7; pLst={}; lim=3000; xMax=Sqrt[lim/m]; yMax=Sqrt[lim/n]; Do[p=m*x^2+n*y^2; If[p<lim && PrimeQ[p], AppendTo[pLst, p]], {x, xMax}, {y, yMax}]; Union[pLst] (T. D. Noe, May 05 2005)
QuadPrimes2[3, 0, 7, 10000] (* see A106856 *)

Prog

(Magma) [p: p in PrimesUpTo(3000) | p mod 84 in [3, 7, 19, 31, 55]]; // Vincenzo Librandi, Jul 19 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=0, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\7), if(isprime(t=w+7*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

Crossrefs

Cf. A102269-A102275, A139827.

Sequence in context: A145472 A217199 A077313 * A145039 A112633 A113916

Adjacent sequences: A102268 A102269 A102270 * A102272 A102273 A102274

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 19 2005

Status

approved