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

1,1

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)

Formula

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A241081 A188173 A142411 * A155572 A356246 A107145

Adjacent sequences: A139921 A139922 A139923 * A139925 A139926 A139927

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved