A243177 Numbers of the form 3x^2+2xy+3y^2.

0, 3, 4, 8, 11, 12, 16, 19, 24, 27, 32, 36, 43, 44, 48, 51, 59, 64, 67, 68, 72, 75, 76, 83, 88, 96, 99, 100, 107, 108, 123, 128, 131, 132, 136, 139, 144, 147, 152, 163, 164, 171, 172, 176, 179, 187, 192, 196, 200, 204, 211, 216, 219, 227, 228, 236, 243, 251, 256, 264, 267, 268, 272, 275, 283, 288, 291, 292, 300, 304, 307, 323, 324, 328, 331, 332, 339, 344, 347

Offset

1,2

Comments

Discriminant -32.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

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

Naoki Uchida, Integers of the Form ax^2 + bxy + cy^2 (2020 preprint)

Mathematica

ofTheFormQ[n_] := Reduce[n == 3*x^2 + 2*x*y + 3*y^2, {x, y}, Integers] =!= False; Select[Range[0, 400], ofTheFormQ] (* Jean-François Alcover, Jun 04 2014 *)

Prog

(PARI) is(n)=if(n==0, return(1)); my(h=valuation(n, 2), f=factor(n>>h), s); if(h==1, return(0)); for(i=1, #f~, if(f[i, 1]%8==3, s+=f[i, 2], f[i, 1]%8>3 && f[i, 2]%2, return(0))); h>1 || s%2 \\ Charles R Greathouse IV, Feb 10 2020

Crossrefs

Primes: A007520.

Sequence in context: A310011 A047458 A004014 * A113294 A169691 A255748

Adjacent sequences: A243174 A243175 A243176 * A243178 A243179 A243180

Keyword

nonn

Author

N. J. A. Sloane, Jun 02 2014

Status

approved