A374094 a(n) is the smallest nonnegative integer k where there are exactly n solutions to x^2 + x*y + y^2 = k with 0 < x < y.

0, 7, 91, 637, 1729, 31213, 12103, 405769, 53599, 157339, 593047

Offset: 0

Author

Seiichi Manyama, Jun 28 2024

Keywords

• nonn
• more

Comments

a(n) is the smallest nonnegative k such that A374092(k) = n.

a(11) > 10^8. - Robert Israel, Jun 28 2024

Crossrefs

Cf. A093195, A374095.

Cf. A374090, A374092.

Programs

Maple

N:= 10^6:
V:= Array(0..N):
for x from 1 to floor(sqrt(N/3)) do
  for y from x+1 do
     v:= x^2 + x*y + y^2;
     if v > N then break fi;
     V[v]:= V[v]+1;
od od:
W:= Array(0..10);
for i from 1 to N while count < 11 do
  v:= V[i];
  if W[v] = 0 then W[v]:= i; count:= count+1 fi
od:
0, seq(W[i],i=1..10); # Robert Israel, Jun 28 2024

Python

from itertools import count
from sympy.abc import x,y
from sympy.solvers.diophantine.diophantine import diop_quadratic
def A374094(n): return next(m for m in count(0) if sum(1 for d in diop_quadratic(x*(x+y)+y**2-m) if 0Chai Wah Wu, Jun 28 2024

Formula

a(n) <= 13 * 7^(n-1).