A107191 Primes of the form 5x^2 + 16y^2.

5, 61, 109, 149, 269, 389, 421, 661, 701, 821, 829, 1069, 1181, 1301, 1381, 1429, 1901, 1949, 2141, 2221, 2269, 2309, 2341, 2381, 2549, 2741, 2749, 2789, 2909, 3061, 3109, 3181, 3221, 3229, 3541, 3701, 3709, 4261, 4349, 4421, 4909, 5189

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -320. 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)

Programs

Mathematica

QuadPrimes2[5, 0, 16, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\5), w=5*x^2; for(y=0, sqrtint((lim-w)\16), if(isprime(t=w+16*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017