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Negated discriminants of orders of imaginary quadratic fields with 1 class per genus (a finite sequence).
(Formerly M2331 N0922)
6

%I M2331 N0922 #35 Dec 03 2019 03:22:03

%S 3,4,7,8,11,12,15,16,19,20,24,27,28,32,35,36,40,43,48,51,52,60,64,67,

%T 72,75,84,88,91,96,99,100,112,115,120,123,132,147,148,160,163,168,180,

%U 187,192,195,228,232,235,240,267,280,288,312,315,340,352,372,403

%N Negated discriminants of orders of imaginary quadratic fields with 1 class per genus (a finite sequence).

%C It is conjectured that a(101) = 7392 is the last term. If it would exist, a(102) > 10^6. - _Hugo Pfoertner_, Dec 01 2019

%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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H Andrew Howroyd, <a href="/A003171/b003171.txt">Table of n, a(n) for n = 1..101</a>

%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 Jianing Song, <a href="/A003171/a003171.txt">List of the corresponding class groups</a>

%o (PARI) ok(n)={(-n)%4<2 && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ _Andrew Howroyd_, Jul 20 2018

%Y Cf. A000926, A133288.

%Y The fundamental terms are given in A003644.

%K nonn,fini

%O 1,1

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

%E Terms a(44) and beyond from _Andrew Howroyd_, Jul 20 2018