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Search: id:A106753
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| A106753 |
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Discriminants, negated, of definite binary quadratic forms. |
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+0
1
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| 3, 7, 8, 11, 12, 15, 19, 20, 23, 24, 27, 28, 31, 32, 35, 39, 40, 43, 44, 47, 48, 51, 52, 55, 56, 59, 60, 63, 67, 68, 71, 72, 75, 76, 79, 80, 83, 84, 87, 88, 91, 92, 95, 96, 99, 103, 104, 107, 108, 111, 112, 115, 116, 119, 120, 123, 124, 127, 128, 131, 132, 135, 136, 139
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A definite binary quadratic form a*x^2 + b*x*y + c*y^2 over the integers has discriminant D = b^2 - 4*a*c < 0; -D is assumed to be a nonsquare.
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FORMULA
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-a(n) is 0 (mod 4) or 1 (mod 4), but not a square.
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MATHEMATICA
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Select[ Range[148], (Mod[ -#, 4] == 0 || Mod[ -#, 4] == 1) && !IntegerQ[Sqrt[ # ]] & ]
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CROSSREFS
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Cf. A014601, A042948 (with squares), A079896 (indefinite case).
Sequence in context: A003607 A087859 A050010 this_sequence A062863 A078466 A047528
Adjacent sequences: A106750 A106751 A106752 this_sequence A106754 A106755 A106756
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KEYWORD
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easy,nonn
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AUTHOR
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S. R. Finch (Steven.Finch(AT)inria.fr), May 16 2005
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