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A014602
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Discriminants of imaginary quadratic fields with class number 1 (negated).
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27
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OFFSET
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1,1
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COMMENTS
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Only fundamental discriminants are listed. The non-fundamental discriminants -12, -16, -27, and -28 also have class number 1 (and there are no others). [From Andrew V. Sutherland (drew(AT)math.mit.edu), Apr 19 2009]
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REFERENCES
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H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 229.
D. A. Cox, Primes of the form x^2+ny^2, Wiley, p. 271.
J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, see p. 483.
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LINKS
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Table of n, a(n) for n=1..9.
Eric Weisstein's World of Mathematics, Class Number
Index entries for sequences related to quadratic fields
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MATHEMATICA
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Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] &) /@ Select[ Range[200], NumberFieldClassNumber[ Sqrt[-#]] == 1 &]] (* From Jean-François Alcover, Jan 04 2012 *)
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PROG
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(PARI) is(n)=isfundamental(-n) && qfbclassno(-n)==1 \\ Charles R Greathouse IV, Nov 20 2012
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CROSSREFS
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Cf. A003173, A013658, A014603, A046002, ..., A046020.
Sequence in context: A192051 A033195 A050032 * A078823 A045615 A211220
Adjacent sequences: A014599 A014600 A014601 * A014603 A014604 A014605
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KEYWORD
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nonn,fini,full,nice
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AUTHOR
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Eric Rains (rains(AT)caltech.edu)
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STATUS
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approved
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