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Discriminants of the known imaginary quadratic fields with 1 class per genus (a finite sequence).
(Formerly M2333)
6

%I M2333 #25 Jul 20 2018 17:34:59

%S 3,4,7,8,11,15,19,20,24,35,40,43,51,52,67,84,88,91,115,120,123,132,

%T 148,163,168,187,195,228,232,235,267,280,312,340,372,403,408,420,427,

%U 435,483,520,532,555,595,627,660,708,715,760,795,840,1012,1092,1155,1320,1380,1428,1435,1540,1848,1995,3003,3315,5460

%N Discriminants of the known imaginary quadratic fields with 1 class per genus (a finite sequence).

%C This is the complete table from Borevich and Shafarevich.

%C If the GRH is true, the list contains the discriminants of all imaginary quadratic fields with 1 class per genus; otherwise, there may be one more such discriminant not on the list. (See Weinberger.) - _Everett W. Howe_, Aug 01 2014

%D Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 425-430.

%D L. E. Dickson, Introduction to the Theory of Numbers. Dover, NY, 1957, p. 85.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Rick L. Shepherd, <a href="http://libres.uncg.edu/ir/uncg/f/Shepherd_uncg_0154M_11099.pdf">Binary quadratic forms and genus theory</a>, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.

%H P. J. Weinberger, <a href="http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-aav22i2p117bwm">Exponents of the class groups of complex quadratic fields</a>, Acta Arith. 22 (1973), 117-124.

%o (PARI) ok(n)={isfundamental(-n) && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ _Andrew Howroyd_, Jul 20 2018

%Y Cf. A133288, A316743.

%K nonn,fini,full,nice

%O 1,1

%A _N. J. A. Sloane_, _Mira Bernstein_

%E Clarified name (added "the known") - _Everett W. Howe_, Aug 01 2014