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A198773 Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=y.

%I A198773 #16 Jun 21 2018 10:32:47
%S A198773 49,91,133,147,169,196,217,247,259,273,301,343,361,364,399,403,427,
%T A198773 441,469,481,507,511,532,553,559,588,589,651,676,679,703,721,741,763,
%U A198773 777,784,793,817,819,868,871,889,903,949,961,973,988,1027,1029,1036,1057,1083,1092,1099,1141,1147
%N A198773 Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=y.
%C A198773 A088534(a(n)) = 2; subsequence of A118886, see also A003136.
%H A198773 Reinhard Zumkeller, <a href="/A198773/b198773.txt">Table of n, a(n) for n = 1..10000</a>
%e A198773 a(10) = 273 = 1^2 + 1*16 + 16^2 = 8^2 + 8*11 + 11^2, A088534(273) = 2;
%e A198773 a(11) = 301 = 4^2 + 4*15 + 15^2 = 9^2 + 9*11 + 11^2, A088534(301) = 2.
%t A198773 amax = 2000; xmax = Sqrt[amax] // Ceiling; Clear[f]; f[_] = 0; Do[q = x^2 + x y + y^2; f[q] = f[q] + 1, {x, 0, xmax}, {y, x, xmax}];
%t A198773 A198773 = Select[Range[0, 3 xmax^2], # <= amax && f[#] == 2&] (* _Jean-François Alcover_, Jun 21 2018 *)
%o A198773 (Haskell)
%o A198773 a198773 n = a198773_list !! (n-1)
%o A198773 a198773_list = filter ((== 2) . a088534) a003136_list
%o A198773 (PARI) is(n)=my(t=#bnfisintnorm(bnfinit(z^2+z+1), n)); t==3 || t==4;
%o A198773 select(n->is(n), vector(1500,j,j)) \\ _Joerg Arndt_, Jan 11 2015
%Y A198773 Cf. A198772, A198774, A198775.
%K A198773 nonn
%O A198773 1,1
%A A198773 _Reinhard Zumkeller_, Oct 30 2011