A247881 Numbers of the form x^2 + 13*y^2.

0, 1, 4, 9, 13, 14, 16, 17, 22, 25, 29, 36, 38, 49, 52, 53, 56, 61, 62, 64, 68, 77, 81, 88, 94, 100, 101, 113, 116, 117, 118, 121, 126, 133, 134, 142, 144, 152, 153, 157, 166, 169, 173, 181, 182, 196, 198, 208, 209, 212, 217, 221, 224, 225, 233, 238, 244, 248, 256, 257, 261, 269

Offset: 1

Author

Alonso del Arte, Sep 25 2014

Keywords

• easy
• nonn

Comments

Norms of numbers in Z[sqrt(-13)].

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033210 (subsequence of primes).

Programs

Maple

N:= 1000: # for terms <= N
S:= {seq(seq(x^2 + 13*y^2, x=0 .. floor(sqrt(N-13*y^2))),y=0..floor(sqrt(N/13)))}:
sort(convert(S,list)); # Robert Israel, Jun 19 2025