A140616 Primes of the form 5x^2+4xy+68y^2.

5, 101, 173, 269, 293, 461, 509, 677, 773, 797, 941, 1013, 1109, 1181, 1277, 1301, 1613, 1637, 1949, 1973, 2141, 2309, 2357, 2477, 2621, 2693, 2789, 2861, 2957, 3461, 3533, 3701, 3797, 3821, 3989, 4133, 4157, 4373, 4493, 4637, 4877, 4973

Offset: 1

Author

T. D. Noe, May 19 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1344. Also primes of the form 5x^2+2xy+101y^2.

In base 12, the sequence is 5, 85, 125, 1X5, 205, 325, 365, 485, 545, 565, 665, 705, 785, 825, 8X5, 905, E25, E45, 1165, 1185, 12X5, 1405, 1445, 1525, 1625, 1685, 1745, 17X5, 1865, 2005, 2065, 2185, 2245, 2265, 2385, 2485, 24X5, 2645, 2725, 2825, 29X5, 2X65, where X is for 10 and E is for 11. Moreover, the discriminant is -940. - Walter Kehowski, May 31 2008

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)

Crossrefs

Cf. A140633.

Programs

Mathematica

Union[QuadPrimes2[5, 4, 68, 10000], QuadPrimes2[5, -4, 68, 10000]] (* see A106856 *)