%I #41 Oct 04 2014 11:08:22

%S 13,17,29,53,61,101,113,157,173,181,233,257,269,277,313,337,373,389,

%T 433,521,569,601,641,653,673,677,701,757,797,809,829,857,881,937,953,

%U 997,1013,1049,1069,1093,1109,1117

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

%C 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

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

%H Vincenzo Librandi and Ray Chandler, <a href="/A033210/b033210.txt">Table of n, a(n) for n = 1..10000</a> [First 3000 terms from Vincenzo Librandi]

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%F 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]

%F a(n) ~ 4n log n. - _Charles R Greathouse IV_, Nov 09 2012

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

%o (PARI) select(n->vecsearch([1,9,13,17,25,29,49],n%52), primes(100)) \\ _Charles R Greathouse IV_, Nov 09 2012

%o (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

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

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.