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Search: id:A003657
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| A003657 |
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Discriminants of imaginary quadratic fields, negated.
(Formerly M2332)
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+0
9
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| 3, 4, 7, 8, 11, 15, 19, 20, 23, 24, 31, 35, 39, 40, 43, 47, 51, 52, 55, 56, 59, 67, 68, 71, 79, 83, 84, 87, 88, 91, 95, 103, 104, 107, 111, 115, 116, 119, 120, 123, 127, 131, 132, 136, 139, 143, 148, 151, 152, 155, 159, 163, 164, 167, 168, 179, 183, 184, 187, 191
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Negative of 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 Buell reference pp. 223-234. See 4*A089269 for even a(n) and A039957 for odd a(n). - Wolfdieter Lang, Nov 07 2003
All prime numbers in the set of the absolute values of negative fundamental discriminants are Gaussian primes (A002145). - Paul Muljadi (paulmuljadi(AT)yahoo.com), Mar 29 2008
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989.
H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 514.
P. Ribenboim, Algebraic Numbers, Wiley, NY, 1972, p. 97.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..3000
S. R. Finch, Class number theory
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Fundamental Discriminant
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CROSSREFS
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Cf. A002145.
Sequence in context: A067186 A133675 A050122 this_sequence A003644 A033195 A107819
Adjacent sequences: A003654 A003655 A003656 this_sequence A003658 A003659 A003660
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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