A243175 Numbers of the form x^2 + xy + 7y^2.

0, 1, 4, 7, 9, 13, 16, 19, 25, 27, 28, 31, 36, 37, 43, 49, 52, 61, 63, 64, 67, 73, 76, 79, 81, 91, 97, 100, 103, 108, 109, 112, 117, 121, 124, 127, 133, 139, 144, 148, 151, 157, 163, 169, 171, 172, 175, 181, 189, 193, 196, 199, 208, 211, 217, 223, 225, 229, 241, 243, 244, 247, 252, 256, 259, 268, 271, 277, 279, 283, 289, 292, 301, 304, 307, 313, 316, 324, 325

Offset: 1

Author

N. J. A. Sloane, Jun 02 2014

Keywords

• nonn

Comments

Discriminant -27.

From Jianing Song, Mar 13 2021: (Start)

Numbers in A003136 that are not congruent to 3 modulo 9.

Closed under multiplication.

For k > 0, k is a term if and only if: write k = 3^a * Product_{i=1..r} (p_i)^(a_i) * Product_{i=1..s} (q_i)^(b_i), p_i == 1 (mod 3), q_i == 2 (mod 3) are primes, then a != 1 and each b_i is even. (End)

Links

• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes: A002476.

Cf. A003136.

Programs

Mathematica

Select[Range[0, 350], Resolve@Exists[{x, y}, Reduce[# == (x^2 + x y + 7 y^2), {x, y}, Integers]] &] (* Vincenzo Librandi, Feb 11 2020 *)