A033220 Primes of form x^2+30*y^2.

31, 79, 151, 199, 241, 271, 409, 439, 601, 631, 751, 769, 919, 991, 1009, 1039, 1129, 1201, 1231, 1249, 1279, 1321, 1399, 1471, 1489, 1609, 1759, 1801, 1831, 1879, 1951, 1999, 2089, 2161, 2239, 2281

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.

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)

Crossrefs

Cf. A139643.

Programs

Magma

[ p: p in PrimesUpTo(3000) | p mod 120 in {1, 31, 49, 79} ]; // Vincenzo Librandi, Jul 20 2012

Mathematica

QuadPrimes2[1, 0, 30, 10000] (* see A106856 *)

PARI

select(n->vecsearch([1,31,49,79],n%120), primes(400)) \\ Charles R Greathouse IV, Nov 09 2012

Formula

Equivalently, primes congruent to {1, 31, 49, or 79} (mod 120) - T. D. Noe, Apr 29 2008. [See e.g. Cox, p. 36. - N. J. A. Sloane, May 27 2014]

a(n) ~ 8n log n. - Charles R Greathouse IV, Nov 09 2012