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Search: id:A003658
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| A003658 |
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Fundamental discriminants of real quadratic fields; indices of primitive positive Dirichlet L-series.
(Formerly M3776)
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+0
7
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| 1, 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40, 41, 44, 53, 56, 57, 60, 61, 65, 69, 73, 76, 77, 85, 88, 89, 92, 93, 97, 101, 104, 105, 109, 113, 120, 124, 129, 133, 136, 137, 140, 141, 145, 149, 152, 156, 157, 161, 165, 168, 172, 173, 177, 181, 184, 185, 188, 193
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All the prime numbers in the set of positive fundamental discriminants are Pythagorean primes (A002144). - Paul Muljadi (paulmuljadi(AT)yahoo.com), Mar 28 2008
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REFERENCES
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H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 505.
M. Pohst and Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, page 432.
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..3001
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, Fundamental Discriminant
Eric Weisstein's World of Mathematics, Class Number
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FORMULA
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Square-free numbers (multiplied by 4 if not = 1 mod 4).
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PROGRAM
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(PARI) v=[]; for(n=1, 500, if(isfundamental(n), v=concat(v, n))); v
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CROSSREFS
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Cf. A003657.
Cf. A002144.
Adjacent sequences: A003655 A003656 A003657 this_sequence A003659 A003660 A003661
Sequence in context: A116602 A079896 A133315 this_sequence A003656 A003246 A124378
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Mira Bernstein, Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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More terms from Eric Weisstein (eric(AT)weisstein.com) and Jason Earls (jcearls(AT)cableone.net), Jun 19 2001
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