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A374159 a(n) is the smallest nonnegative integer k where exactly n pairs of positive integers (x, y) exist such that x^2 + 7*y^2 = k.

%I A374159 #17 Jun 30 2024 11:20:38
%S A374159 0,8,32,128,352,704,1408,2816,5632,11264,16192,45056,32384,123904,
%T A374159 64768,178112,129536,2883584,259072,1982464,469568,712448,1036288,
%U A374159 184549376,939136,21551552,4145152,2849792,1878272
%N A374159 a(n) is the smallest nonnegative integer k where exactly n pairs of positive integers (x, y) exist such that x^2 + 7*y^2 = k.
%C A374159 a(n) is the smallest nonnegative k such that A216511(k) = n.
%C A374159 Conjecture: All terms are multiple of a(1) = 8.
%C A374159 a(30) = 5165248.
%C A374159 a(31) = 16386304.
%C A374159 a(32) = 3756544.
%C A374159 a(33) = 11399168.
%C A374159 a(34) = 66322432.
%C A374159 a(35) = 86206208.
%C A374159 a(36) = 7513088.
%o A374159 (Python)
%o A374159 from itertools import count
%o A374159 from sympy.abc import x, y
%o A374159 from sympy.solvers.diophantine.diophantine import diop_quadratic
%o A374159 def A374159(n): return next(m for m in count(0) if sum(1 for d in diop_quadratic(x**2+7*y**2-m) if d[0]>0 and d[1]>0)==n) # _Chai Wah Wu_, Jun 30 2024
%Y A374159 Cf. A328151, A343105, A374158, A374160, A374161.
%Y A374159 Cf. A216511.
%K A374159 nonn,more
%O A374159 0,2
%A A374159 _Seiichi Manyama_, Jun 29 2024