A139862 Primes of the form 5x^2 + 26y^2.

5, 31, 71, 109, 149, 151, 229, 239, 271, 349, 359, 421, 431, 461, 479, 509, 541, 631, 661, 709, 821, 839, 941, 1021, 1061, 1151, 1181, 1229, 1279, 1319, 1399, 1471, 1549, 1669, 1709, 1789, 1831, 1861, 1879, 2039, 2069, 2111, 2221, 2269, 2309

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 {5, 21, 31, 71, 109, 111, 119, 141, 149, 151, 189, 229, 239, 271, 279, 301, 319, 349, 359, 421, 431, 461, 479, 501, 509} (mod 520).

Mathematica

QuadPrimes2[5, 0, 26, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 520 in {5, 21, 31, 71, 109, 111, 119, 141, 149, 151, 189, 229, 239, 271, 279, 301, 319, 349, 359, 421, 431, 461, 479, 501, 509}]; // Vincenzo Librandi, Jul 29 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)\26), if(isprime(t=w+26*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 07 2017

Crossrefs

Sequence in context: A333243 A078686 A031908 * A299505 A102732 A213068

Adjacent sequences: A139859 A139860 A139861 * A139863 A139864 A139865

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved