A139983 Primes of the form 29x^2+18xy+29y^2.

29, 109, 181, 269, 421, 509, 661, 829, 941, 1021, 1181, 1229, 1381, 1549, 1709, 1741, 1789, 1861, 2029, 2141, 2269, 2309, 2389, 2549, 2621, 2749, 2789, 2909, 3061, 3109, 3181, 3221, 3229, 3301, 3461, 3701, 3821, 3989, 4021, 4421, 4549

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-3040. See A139827 for more information.

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)

Programs

Magma

[p: p in PrimesUpTo(6000) | p mod 3040 in [21, 29, 69, 109, 141, 181, 189, 221, 261, 269, 341, 421, 469, 509, 621, 629, 661, 749, 781, 789, 829, 869, 901, 941, 949, 981, 1021, 1029, 1101, 1181, 1229, 1269, 1381, 1389, 1421, 1509, 1541, 1549, 1589, 1629, 1661, 1701, 1709, 1741, 1781, 1789, 1861, 1941, 1989, 2029, 2141, 2149, 2181, 2269, 2301, 2309, 2349, 2389, 2421, 2461, 2469, 2501, 2541, 2549, 2621, 2701, 2749, 2789, 2901, 2909, 2941, 3029]]; // Vincenzo Librandi, Aug 03 2012

Mathematica

Union[QuadPrimes2[29, 18, 29, 10000], QuadPrimes2[29, -18, 29, 10000]] (* see A106856 *)

Formula

The primes are congruent to {21, 29, 69, 109, 141, 181, 189, 221, 261, 269, 341, 421, 469, 509, 621, 629, 661, 749, 781, 789, 829, 869, 901, 941, 949, 981, 1021, 1029, 1101, 1181, 1229, 1269, 1381, 1389, 1421, 1509, 1541, 1549, 1589, 1629, 1661, 1701, 1709, 1741, 1781, 1789, 1861, 1941, 1989, 2029, 2141, 2149, 2181, 2269, 2301, 2309, 2349, 2389, 2421, 2461, 2469, 2501, 2541, 2549, 2621, 2701, 2749, 2789, 2901, 2909, 2941, 3029} (mod 3040).