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A003656
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Discriminants of real quadratic fields with unique factorization.
(Formerly M3777)
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13
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5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 41, 44, 53, 56, 57, 61, 69, 73, 76, 77, 88, 89, 92, 93, 97, 101, 109, 113, 124, 129, 133, 137, 141, 149, 152, 157, 161, 172, 173, 177, 181, 184, 188, 193, 197, 201, 209, 213, 217, 233, 236, 237, 241, 248, 249, 253, 268, 269
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Real quadratic number fields with class number 1
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REFERENCES
| D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.
H. Cohen, Advanced Topics in Computational Number Theory, Springer, 2000, p. 534.
H. Hasse, Number Theory, Springer-Verlag, NY, 1980, p. 576.
Pohst and Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, page 432.
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..1000
Henri Cohen and X.-F. Roblot, Computing the Hilbert Class Field of Real Quadratic Fields, Math. Comp. 69 (2000), 1229-1244.
Eric Weisstein's World of Mathematics, Class Number
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MATHEMATICA
| maxDisc = 269; t = Table[ {NumberFieldDiscriminant[ Sqrt[n] ], NumberFieldClassNumber[ Sqrt[n] ]}, {n, Select[ Range[2, maxDisc], SquareFreeQ] } ]; Union[ Select[ t, #[[2]] == 1 && #[[1]] <= maxDisc & ][[All, 1]]] (* From Jean-François Alcover, Jan 24 2012 *)
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CROSSREFS
| Cf. A035120.
Sequence in context: A079896 A133315 A003658 * A003246 A143748 A124378
Adjacent sequences: A003653 A003654 A003655 * A003657 A003658 A003659
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 15 2002
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