A033210 Primes of the form x^2+13*y^2.

13, 17, 29, 53, 61, 101, 113, 157, 173, 181, 233, 257, 269, 277, 313, 337, 373, 389, 433, 521, 569, 601, 641, 653, 673, 677, 701, 757, 797, 809, 829, 857, 881, 937, 953, 997, 1013, 1049, 1069, 1093, 1109, 1117

Offset

1,1

Comments

First differences are multiples of 4 (which follows from set of differences of the moduli in the Noe formula). Minimal difference 4 occurs at a(1)=17, a(25)=673, a(48)=1297, etc. - Zak Seidov, Oct 04 2014

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 3000 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, 13, 17, 25, 29, or 49} (mod 52). - T. D. Noe, Apr 29 2008 [See e.g. Cox, p. 36. - N. J. A. Sloane, May 27 2014]

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

Mathematica

QuadPrimes2[1, 0, 13, 10000] (* see A106856 *)

Prog

(PARI) select(n->vecsearch([1, 9, 13, 17, 25, 29, 49], n%52), primes(100)) \\ Charles R Greathouse IV, Nov 09 2012
(PARI) is_A033210(n)={vecsearch([1, 9, 13, 17, 25, 29, 49], n%52)&&isprime(n)} \\ setsearch() is still slower by a factor > 2. - M. F. Hasler, Oct 04 2014

Crossrefs

Cf. A139643, A248212 (x) and A248213 (y).

Sequence in context: A048520 A283407 A283358 * A274506 A107159 A138375

Adjacent sequences: A033207 A033208 A033209 * A033211 A033212 A033213

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved