A107179 Primes of the form 5x^2 + 14y^2.

5, 19, 59, 61, 101, 131, 139, 181, 229, 251, 269, 349, 419, 461, 509, 619, 661, 691, 811, 829, 859, 941, 971, 1021, 1069, 1091, 1109, 1181, 1259, 1291, 1301, 1459, 1531, 1571, 1669, 1699, 1741, 1811, 1861, 1931, 1949, 1979, 2029, 2099, 2131

Offset

1,1

Comments

Discriminant = -280. See A107132 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, 19, 59, 61, 69, 101, 131, 139, 171, 181, 229, 251, 269} (mod 280). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[5, 0, 14, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 280 in {5, 19, 59, 61, 69, 101, 131, 139, 171, 181, 229, 251, 269} ]; // Vincenzo Librandi, Jul 26 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)\14), if(isprime(t=w+14*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A139827.

Sequence in context: A109415 A029861 A224034 * A332720 A092442 A341711

Adjacent sequences: A107176 A107177 A107178 * A107180 A107181 A107182

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved