A139869 Primes of the form 5x^2 + 33y^2.

5, 53, 113, 137, 257, 317, 353, 617, 653, 773, 797, 977, 1013, 1193, 1277, 1373, 1433, 1637, 1697, 1973, 2237, 2297, 2333, 2357, 2633, 2693, 2753, 2777, 2897, 2957, 3257, 3413, 3557, 3617, 3677, 3833, 3917, 4013, 4073, 4217, 4337, 4493

Offset

1,1

Comments

Discriminant = -660. See A139827 for more information.

Links

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

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Formula

The primes are congruent to {5, 53, 113, 137, 257, 317, 353, 377, 533, 617, 653} (mod 660).

Mathematica

QuadPrimes2[5, 0, 33, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(6000) | p mod 660 in {5, 53, 113, 137, 257, 317, 353, 377, 533, 617, 653}]; // Vincenzo Librandi, Jul 30 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\5), w=5*x^2; for(y=0, sqrtint((lim-w)\33), if(isprime(t=w+33*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 07 2017

Crossrefs

Sequence in context: A091272 A142399 A107004 * A072156 A101190 A201017

Adjacent sequences: A139866 A139867 A139868 * A139870 A139871 A139872

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved