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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.
4
0, 7, 91, 637, 1729, 31213, 12103, 405769, 53599, 157339, 593047
OFFSET
0,2
COMMENTS
a(n) is the smallest nonnegative k such that A374092(k) = n.
a(11) > 10^8. - Robert Israel, Jun 28 2024
FORMULA
a(n) <= 13 * 7^(n-1).
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
PROG
(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 0<d[0]<d[1]) == n) # Chai Wah Wu, Jun 28 2024
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Seiichi Manyama, Jun 28 2024
STATUS
approved