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Search: id:A089269
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| A089269 |
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One fourth of negative of even fundamental discriminants of definite quadratic forms. |
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+0
3
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| 1, 2, 5, 6, 10, 13, 14, 17, 21, 22, 26, 29, 30, 33, 34, 37, 38, 41, 42, 46, 53, 57, 58, 61, 62, 65, 66, 69, 70, 73, 74, 77, 78, 82, 85, 86, 89, 93, 94, 97, 101, 102, 105, 106, 109, 110, 113, 114, 118, 122, 129, 130, 133, 134, 137, 138, 141, 142, 145, 146, 149, 154, 157
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = the fundamental discriminants D := b^2-4*a*c<0 of definite integer binary quadratic forms F=a*x^2+b*x*y+c*y^2. See A039957 for the odd numbers and A003657 for the combined even and odd numbers.
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REFERENCES
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D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 231-234.
A. Scholz and B. Schoeneberg, Einfuehrung in die Zahlentheorie, 5. Aufl., de Gruyter, Berlin, New York, 1973, ch.30.
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FORMULA
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a(n)=d(n)/4 with mod(d, 4)=0, d>0, and if d/4 is odd then mod(d/4, 4)=1 with d/4 squarefree, and if d/4 is even then d/8 odd and squarefree. For the squarefree numbers see A005117.
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CROSSREFS
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Adjacent sequences: A089266 A089267 A089268 this_sequence A089270 A089271 A089272
Sequence in context: A064572 A032399 A007969 this_sequence A047440 A007674 A086719
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KEYWORD
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nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Nov 07 2003
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