A102271 Primes of the form 3*x^2 + 7*y^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, 2287, 2371, 2383
Offset: 1
Links
- 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)
Programs
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Magma
[p: p in PrimesUpTo(3000) | p mod 84 in [3, 7, 19, 31, 55]]; // Vincenzo Librandi, Jul 19 2012
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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[pT. D. Noe, May 05 2005 *) QuadPrimes2[3, 0, 7, 10000] (* see A106856 *) -
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
Formula
The primes are congruent to {3, 7, 19, 31, 55} (mod 84). - T. D. Noe, May 02 2008
Comments