A139863 Primes of the form 10x^2 + 13y^2.

13, 23, 53, 103, 127, 157, 173, 263, 277, 367, 373, 503, 607, 647, 653, 677, 727, 757, 797, 823, 887, 997, 1013, 1063, 1093, 1117, 1213, 1223, 1277, 1303, 1327, 1447, 1453, 1543, 1583, 1613, 1637, 1663, 1693, 1733, 1823, 1847, 1933, 1973, 2053

Offset

1,1

Comments

Discriminant = -520. 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 {13, 23, 53, 77, 87, 103, 127, 133, 157, 173, 183, 207, 237, 263, 277, 287, 303, 367, 373, 407, 413, 477, 493, 503, 517} (mod 520).

Mathematica

QuadPrimes2[10, 0, 13, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 520 in {13, 23, 53, 77, 87, 103, 127, 133, 157, 173, 183, 207, 237, 263, 277, 287, 303, 367, 373, 407, 413, 477, 493, 503, 517}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=0, sqrtint(lim\10), w=10*x^2; for(y=1, sqrtint((lim-w)\13), if(isprime(t=w+13*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 07 2017

Crossrefs

Sequence in context: A103166 A154863 A194156 * A304672 A316119 A046862

Adjacent sequences: A139860 A139861 A139862 * A139864 A139865 A139866

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved