A139924 Primes of the form 8x^2+8xy+41y^2.

41, 89, 137, 281, 353, 401, 449, 593, 617, 761, 929, 977, 1097, 1217, 1289, 1409, 1553, 1601, 1697, 1721, 1913, 2153, 2273, 2633, 2657, 2777, 2801, 2897, 2969, 3089, 3209, 3257, 3593, 3833, 3881, 4049, 4217, 4337, 4409, 4457, 4649, 4673

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1248. See A139827 for more information.

Also primes of the forms 32x^2+16xy+41y^2 and 20x^2+12xy+33y^2. See A140633. - T. D. Noe, May 19 2008

In base 12, the sequence is 35, 75, E5, 1E5, 255, 295, 315, 415, 435, 535, 655, 695, 775, 855, 8E5, 995, X95, E15, E95, EE5, 1135, 12E5, 1395, 1635, 1655, 1735, 1755, 1815, 1875, 1955, 1X35, 1X75, 20E5, 2275, 22E5, 2415, 2535, 2615, 2675, 26E5, 2835, 2855. Moreover, the discriminant is 880 and all primes are {35, 75, E5, 115, 1E5, 215} mod 220. - 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)

Programs

Magma

[ p: p in PrimesUpTo(6000) | p mod 312 in [41, 89, 137, 161, 281, 305]]; // Vincenzo Librandi, Aug 01 2012

Mathematica

QuadPrimes2[8, -8, 41, 10000] (* see A106856 *)

Formula

The primes are congruent to {41, 89, 137, 161, 281, 305} (mod 312).