Search: id:A003173
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%I A003173 M0827
%S A003173 1,2,3,7,11,19,43,67,163
%N A003173 Heegner numbers: imaginary quadratic fields with unique factorization 
               (or class number 1).
%C A003173 Could also be called Gauss numbers, since he discovered them. Heegner 
               proved list is complete. - Artur Jasinski (grafix(AT)csl.pl), Mar 
               21 2003
%C A003173 n such that Q(sqrt(-n)) has unique factorization into primes.
%D A003173 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 
               1996, p. 224.
%D A003173 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, p. 213.
%D A003173 Heegner K., 1952. Diophantische Analysis und Modulfunktionen. Matematische 
               Zeitschrift Vol. 56 p. 227-253. [From Artur Jasinski (grafix(AT)csl.pl), 
               Oct 21 2008]
%D A003173 W. W. J. Hulsbergen, Conjectures in Arithmetic Algebraic Geometry, Vieweg, 
               1994, p. 8.
%D A003173 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).
%D A003173 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003173 H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, 
               p. 295.
%H A003173 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GausssClassNumberProblem.html">Link to a section of The World of 
               Mathematics.</a> [Yes, 3 s's in that URL]
%H A003173 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HeegnerNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A003173 <a href="Sindx_Qua.html#quadfield">Index entries for sequences related 
               to quadratic fields</a>
%H A003173 Wikipedia, <a href="http://en.wikipedia.org/wiki/Heegner_number">Heegner 
               number</a>
%Y A003173 Cf. A014602 (for discriminants of these fields), A005847 (for class number 
               2).
%Y A003173 Sequence in context: A079739 A158709 A055502 this_sequence A159262 A160434 
               A139630
%Y A003173 Adjacent sequences: A003170 A003171 A003172 this_sequence A003174 A003175 
               A003176
%K A003173 fini,nonn,full,nice
%O A003173 1,2
%A A003173 N. J. A. Sloane (njas(AT)research.att.com).

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