A395310 Prime numbers of the form 11*x^2 - 4*x*y + 20*y^2 where x and y are positive integers.

83, 107, 179, 491, 563, 1091, 1259, 1283, 1307, 1619, 1787, 1907, 1979, 2003, 2099, 2267, 2531, 2843, 3011, 3083, 3323, 3491, 3803, 3851, 3923, 4091, 4139, 4451, 4643, 4787, 4931, 5051, 5171, 5843, 5939, 5987, 6011, 6659, 6827, 6899, 7019, 7211, 7331, 7883, 7907

Offset

1,1

Comments

The discriminant is -864.

All terms are congruent to 11 modulo 24.

Links

Steven Lu, Table of n, a(n) for n = 1..10000

Example

83 = 11 * 1^2 - 4 * 1 * 2 + 20 * 2^2.
107 = 11 * 3^2 - 4 * 3 * 1 + 20 * 1^2.
179 = 11 * 1^2 - 4 * 1 * 3 + 20 * 3^2.

Mathematica

With[{limit = 8000},
 Sort[DeleteDuplicates[
   Select[Flatten[
     Table[11 x^2 - 4 x y + 20 y^2, {x,
       Floor[Sqrt[20 limit/216]]}, {y, Floor[Sqrt[11 limit/216]]}]],
    PrimeQ[#] && # < limit &]]]]

Crossrefs

Cf. A379881, this sequence, A395311 and {3, 11} is a partition of A107007.

Sequence in context: A139765 A031412 A033252 * A347226 A261449 A288880

Adjacent sequences: A395307 A395308 A395309 * A395311 A395312 A395313

Keyword

nonn

Author

Steven Lu, Apr 19 2026

Status

approved