A139530 Primes of the form 24*k + 13.

13, 37, 61, 109, 157, 181, 229, 277, 349, 373, 397, 421, 541, 613, 661, 709, 733, 757, 829, 853, 877, 997, 1021, 1069, 1093, 1117, 1213, 1237, 1381, 1429, 1453, 1549, 1597, 1621, 1669, 1693, 1741, 1789, 1861, 1933, 2029, 2053, 2221, 2269, 2293, 2341, 2389

Offset: 1

Author

Artur Jasinski, Apr 25 2008

Keywords

• nonn

Comments

Primes of the form 4x^2+4xy+13y^2. Discriminant=-192. - T. D. Noe, May 02 2008

Also, primes of form u^2+12v^2 with odd v, while A107008 (which is also expressible as x^2+48y^2) has even v. One can transform its form as (2x+y)^2+12y^2 (where y can only be odd), while the second is x^2+12(2y)^2. Both sequences are 1 mod 12 and together they are primes x^2+12y^2 (A068228). [Tito Piezas III, Jan 01 2009]

Links

• Robert Price, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A139827.

Programs

Mathematica

a = {}; Do[If[PrimeQ[24 n + 13], AppendTo[a, 24 n + 13]], {n, 0, 200}]; a
Select[24Range[0,150]+13,PrimeQ]  (* Harvey P. Dale, Mar 11 2011 *)