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A198773
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Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=y.
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8
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49, 91, 133, 147, 169, 196, 217, 247, 259, 273, 301, 343, 361, 364, 399, 403, 427, 441, 469, 481, 507, 511, 532, 553, 559, 588, 589, 651, 676, 679, 703, 721, 741, 763, 777, 784, 793, 817, 819, 868, 871, 889, 903, 949, 961, 973, 988, 1027, 1029, 1036, 1057, 1083, 1092, 1099, 1141, 1147
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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a(10) = 273 = 1^2 + 1*16 + 16^2 = 8^2 + 8*11 + 11^2, A088534(273) = 2;
a(11) = 301 = 4^2 + 4*15 + 15^2 = 9^2 + 9*11 + 11^2, A088534(301) = 2.
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MATHEMATICA
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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}];
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PROG
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(Haskell)
a198773 n = a198773_list !! (n-1)
a198773_list = filter ((== 2) . a088534) a003136_list
(PARI) is(n)=my(t=#bnfisintnorm(bnfinit(z^2+z+1), n)); t==3 || t==4;
select(n->is(n), vector(1500, j, j)) \\ Joerg Arndt, Jan 11 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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