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A020669
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Numbers of form x^2 + 5 y^2.
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6
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0, 1, 4, 5, 6, 9, 14, 16, 20, 21, 24, 25, 29, 30, 36, 41, 45, 46, 49, 54, 56, 61, 64, 69, 70, 80, 81, 84, 86, 89, 94, 96, 100, 101, 105, 109, 116, 120, 121, 125, 126, 129, 134, 141, 144, 145, 149, 150, 161, 164, 166, 169, 174, 180, 181, 184, 189, 196, 201, 205, 206, 214, 216
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| H. Cohn, A second course in number theory, John Wiley & Sons, Inc., New York-London, 1962. see page 3.
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FORMULA
| Numbers represented by quadratic form with Gram matrix [ 1, 0; 0, 5 ].
List contains 0 and all positive n such that 2*A035170(n)=A028586(2n) is nonzero. - Michael Somos Oct 21 2006
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MATHEMATICA
| formQ[n_] := Reduce[x >= 0 && y >= 0 && n == x^2 + 5 y^2, {x, y}, Integers] =!= False; Select[ Range[0, 300], formQ] (* From Jean-François Alcover, Sep 20 2011 *)
mx = 300; limx = Sqrt[mx]; limy = Sqrt[mx/5]; Select[Union[Flatten[Table[x^2 + 5*y^2, {x, 0, limx}, {y, 0, limy}]]], # <= mx &]] (* T. D. Noe, Sep 20 2011 *)
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CROSSREFS
| Sequence in context: A064931 A073263 A039013 * A091730 A058076 A033819
Adjacent sequences: A020666 A020667 A020668 * A020670 A020671 A020672
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KEYWORD
| easy,nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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