A332335 Numbers of the form 4x^2 + 2xy + 7y^2.

0, 4, 7, 9, 13, 16, 19, 27, 28, 36, 37, 49, 52, 61, 63, 64, 67, 73, 76, 79, 81, 91, 97, 100, 103, 108, 112, 117, 124, 133, 139, 144, 148, 151, 163, 169, 171, 172, 175, 181, 189, 193, 196, 199, 208, 211, 217, 225, 241, 243, 244, 247, 252, 256, 259, 268, 271, 279, 292

Offset

1,2

Comments

Discriminant -108.

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, arXiv:2001.11632 [math.NT], 2020.

Mathematica

Select[Range[0, 300], Resolve@Exists[{x, y}, Reduce[# == (4 x^2 + 2 x y + 7 y^2), {x, y}, Integers]] &] (* Vincenzo Librandi, Feb 11 2020 *)

Prog

(PARI) is(n)=my(h2=valuation(n, 2), h3=valuation(n, 3), f=factor(n>>h2/3^h3), s); if(h2==0 && h3==0, s=1, if(h2%2||h3==1, return(0)); s=0); for(i=1, #f~, if(f[i, 1]%3==1, if(s && !ispower(Mod(2, f[i, 1]), 3), s=0), f[i, 2]%2, return(0))); s==0
(PARI) list(lim)=my(v=List(), t); lim\=1; for(x=0, sqrtint(lim\4), t=4*x^2; for(y=(-x-sqrtint(7*lim-27*x^2))\7, (1-x+sqrtint(7*lim-27*x^2))\7, listput(v, t+2*x*y+7*y^2))); select(n->n<=lim, Set(v))

Crossrefs

Sequence in context: A352272 A229848 A239993 * A310961 A181901 A310962

Adjacent sequences: A332332 A332333 A332334 * A332336 A332337 A332338

Keyword

nonn

Author

Charles R Greathouse IV, Feb 10 2020

Status

approved