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A139863 Primes of the form 10x^2 + 13y^2. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 24 23:23 EDT 2021. Contains 346273 sequences. (Running on oeis4.)