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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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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..3001
S. R. Finch, Class number theory
Eric Weisstein's World of Mathematics, Dirichlet L-Series
Eric Weisstein's World of Mathematics, Fundamental Discriminant
Eric Weisstein's World of Mathematics, Class Number
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FORMULA
| Squarefree numbers (multiplied by 4 if not = 1 mod 4).
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MATHEMATICA
| FundamentalDiscriminantQ[d_] := Module[{m, mod = Mod[d, 4]}, If[mod > 1, Return[False]]; If[mod == 1, Return[SquareFreeQ[d] && d != 1]]; m = d/4; Return[SquareFreeQ[m] && Mod[m, 4] > 1]; ]; Join[{1}, Select[Range[200], FundamentalDiscriminantQ]] (* From Jean-François Alcover, Nov 02 2011, after Eric Weisstein *)
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PROG
| (PARI) v=[]; for(n=1, 500, if(isfundamental(n), v=concat(v, n))); v
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CROSSREFS
| Cf. A003657, A002144.
Sequence in context: A116602 A079896 A133315 * A003656 A003246 A143748
Adjacent sequences: A003655 A003656 A003657 * A003659 A003660 A003661
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| More terms from Eric Weisstein (eric(AT)weisstein.com) and Jason Earls (zevi_35711(AT)yahoo.com), Jun 19 2001
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