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A006203
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Discriminants of imaginary quadratic fields with class number 3 (negated).
(Formerly M5131)
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32
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23, 31, 59, 83, 107, 139, 211, 283, 307, 331, 379, 499, 547, 643, 883, 907
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Also n such that Q(sqrt(-n)) has class number 3. Lubelski in 1936 proved that 907 is maximal term of this sequence. - Artur Jasinski, Oct 07 2011
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REFERENCES
| Lubelski S. 1936 Zur Reduzibilitat von Polynomen in Kongruenzentheorie. Acta Arithmetica 1 pp. 169-183.
H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 514.
Heegner K., 1952. Diophantische Analysis und Modulfunktionen. Matematische Zaitschrift Vol. 56. p. 253. [From Artur Jasinski (grafix(AT)csl.pl), Oct 21 2008]
J. M. Masley, Where are the number fields with small class number?, pp. 221-242 of Number Theory Carbondale 1979, Lect. Notes Math. 751 (1982).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to quadratic fields
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MATHEMATICA
| Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] & ) /@ Select[ Range[1000], NumberFieldClassNumber[ Sqrt[-#]] == 3 & ]] (* From Jean-François Alcover, Jan 04 2012 *)
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PROG
| For PARI code see A005847.
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CROSSREFS
| Cf. A013658, A014602, A014603, A046002, ..., A046020. Cf. also A003173, A005847, ...
Sequence in context: A064792 A030670 A030680 * A153635 A052160 A165985
Adjacent sequences: A006200 A006201 A006202 * A006204 A006205 A006206
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KEYWORD
| fini,nonn,full,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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