A033201 Primes of the form x^2 + 10*y^2.

11, 19, 41, 59, 89, 131, 139, 179, 211, 241, 251, 281, 331, 379, 401, 409, 419, 449, 491, 499, 521, 569, 571, 601, 619, 641, 659, 691, 739, 761, 769, 809, 811, 859, 881, 929, 971, 1009, 1019, 1049, 1051, 1091, 1129, 1171, 1201, 1249, 1259, 1289, 1291, 1321, 1361, 1409, 1451, 1459, 1481

Offset

1,1

References

David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, p. 36.

Links

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 2000 terms from Vincenzo Librandi]

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Formula

Same as primes congruent to 1, 9, 11, or 19 mod 40. See, e.g., Cox, p. 36.

a(n) ~ 4n log n. - Charles R Greathouse IV, Nov 09 2012

Mathematica

Clear[f, lst, p, x, y]; f[x_, y_]:=x^2+10*y^2; lst={}; Do[Do[p=f[x, y]; If[PrimeQ[p]&&p<7212, AppendTo[lst, p]], {y, 0, 6!}], {x, 0, 6!}]; Take[Union[lst], 222] (* Vladimir Joseph Stephan Orlovsky, Aug 04 2009 *)
QuadPrimes2[1, 0, 10, 10000] (* see A106856 *)

Prog

(PARI) select(n->vecsearch([1, 9, 11, 19], n%40), primes(100)) \\ Charles R Greathouse IV, Nov 09 2012
(Magma) [p: p in PrimesUpTo(1500) | NormEquation(10, p) eq true]; // Bruno Berselli, Jul 03 2016

Crossrefs

Cf. A139643.

Primes in A020673.

Sequence in context: A076853 A167475 A136026 * A154386 A066738 A278799

Adjacent sequences: A033198 A033199 A033200 * A033202 A033203 A033204

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved