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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.

%I A374094 #31 Jun 29 2024 10:57:17
%S A374094 0,7,91,637,1729,31213,12103,405769,53599,157339,593047
%N 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.
%C A374094 a(n) is the smallest nonnegative k such that A374092(k) = n.
%C A374094 a(11) > 10^8. - _Robert Israel_, Jun 28 2024
%F A374094 a(n) <= 13 * 7^(n-1).
%p A374094 N:= 10^6:
%p A374094 V:= Array(0..N):
%p A374094 for x from 1 to floor(sqrt(N/3)) do
%p A374094   for y from x+1 do
%p A374094      v:= x^2 + x*y + y^2;
%p A374094      if v > N then break fi;
%p A374094      V[v]:= V[v]+1;
%p A374094 od od:
%p A374094 W:= Array(0..10);
%p A374094 for i from 1 to N while count < 11 do
%p A374094   v:= V[i];
%p A374094   if W[v] = 0 then W[v]:= i; count:= count+1 fi
%p A374094 od:
%p A374094 0, seq(W[i],i=1..10); # _Robert Israel_, Jun 28 2024
%o A374094 (Python)
%o A374094 from itertools import count
%o A374094 from sympy.abc import x,y
%o A374094 from sympy.solvers.diophantine.diophantine import diop_quadratic
%o A374094 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
%Y A374094 Cf. A093195, A374095.
%Y A374094 Cf. A374090, A374092.
%K A374094 nonn,more
%O A374094 0,2
%A A374094 _Seiichi Manyama_, Jun 28 2024