A216277 Primes which cannot be written as x^2 + 5*y^2, where x >= 0, y >= 0.

2, 3, 7, 11, 13, 17, 19, 23, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 211, 223, 227, 233, 239, 251, 257, 263, 271, 277, 283, 293, 307, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 397, 419

Offset: 1

Author

V. Raman, Sep 03 2012

Keywords

• nonn
• easy

Comments

Primes which are not congruent to 1, 5, or 9 (mod 20).

A216286 is the union of {5} and this sequence. - N. J. A. Sloane, Sep 04 2012

References

• David A. Cox, Primes of the Form x^2 + n y^2, Wiley, 1989. See Eq. (1.20), p. 19 and Eq. (2.22), p. 32. - N. J. A. Sloane, Sep 03 2012

Crossrefs

Cf. A033205.

Programs

PARI

list(lim)=my(v=List(),t); forprime(p=2,lim, t=p%20; if(t!=1 && t!=9 && t!=5, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 12 2017

Formula

a(n) ~ 4/3 * n log n. - Charles R Greathouse IV, Jan 12 2017