A020670 Numbers of form x^2 + 7y^2.

0, 1, 4, 7, 8, 9, 11, 16, 23, 25, 28, 29, 32, 36, 37, 43, 44, 49, 53, 56, 63, 64, 67, 71, 72, 77, 79, 81, 88, 92, 99, 100, 107, 109, 112, 113, 116, 121, 127, 128, 137, 144, 148, 149, 151, 161, 163, 169, 172, 175, 176, 179, 184, 191, 193, 196, 197, 200, 203, 207, 211, 212, 224

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

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)

Crossrefs

Cf. A033207.

Programs

Magma

[n: n in [0..230] | NormEquation(7, n) eq true]; // Vincenzo Librandi, Aug 31 2016

Mathematica

lim=250; k=7; Union@Flatten@Table[x^2 + k y^2, {y, 0, Sqrt[lim/k]}, {x, 0, Sqrt[lim-k y^2]}] (* Vincenzo Librandi, Aug 31 2016 *)

PARI

is(n)=my(f=factor(n));for(i=1,#f[,1],if(kronecker(f[i,1],7)<0 && f[i,2]%2, return(0))); n%4!=2 \\ Charles R Greathouse IV, Nov 18 2012