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%I #40 Jun 17 2022 11:48:39
%S 3,4,7,8,11,19,43,67,163
%N Discriminants of imaginary quadratic fields with class number 1 (negated).
%C Only fundamental discriminants are listed. The non-fundamental discriminants -12, -16, -27, and -28 also have class number 1 (and there are no others). - _Andrew V. Sutherland_, Apr 19 2009
%D H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 229.
%D D. A. Cox, Primes of the form x^2+ny^2, Wiley, p. 271.
%D J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, see p. 483.
%H A. Abatzoglou, A. Silverberg, A. V. Sutherland, and A. Wong, <a href="http://arxiv.org/abs/1404.0107">A framework for deterministic primality proving using elliptic curves with complex multiplication</a>, arXiv preprint arXiv:1404.0107 [math.NT], 2014.
%H Giacomo Cherubini and Alessandro Fazzari, <a href="https://arxiv.org/abs/2206.08282">Hyperbolic angles from Heegner points</a>, arXiv:2206.08282 [math.NT], 2022. Mentions this sequence.
%H Charles Delorme and Guillermo Pineda-Villavicencio, <a href="https://www.emis.de/journals/JIS/VOL18/Pineda/pin2.html">Quadratic Form Representations via Generalized Continuants</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.4.
%H Erich Kaltofen and Heinrich Rolletschek, <a href="https://doi.org/10.1090/S0025-5718-1989-0982367-2">Computing greatest common divisors and factorizations in quadratic number fields</a>, Mathematics of Computation 53.188 (1989): 697-720. See page 698.
%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 Carl Ludwig Siegel, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002087030">Zum Beweise des Starkschen Satzes</a>, Inventiones mathematicae 5.3 (1968): 180-191.
%H Harold M. Stark, <a href="https://doi.org/10.1307/mmj/1028999653">A complete determination of the complex quadratic fields of class-number one</a>, The Michigan Mathematical Journal 14.1 (1967): 1-27.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] &) /@ Select[ Range[200], NumberFieldClassNumber[ Sqrt[-#]] == 1 &]] (* _Jean-François Alcover_, Jan 04 2012 *)
%o (PARI) is(n)=isfundamental(-n) && qfbclassno(-n)==1 \\ _Charles R Greathouse IV_, Nov 20 2012
%o (Sage)
%o is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 1
%o A014602 = lambda n: filter(is_fund_and_qfbcn_1, (-1,-2,..-n))
%o [-n for n in A014602(270)] # _Peter Luschny_, Aug 10 2014
%Y Cf. A003656 (real case), A003173, A013658, A014603, A046002...A046020.
%K nonn,fini,full,nice
%O 1,1
%A Eric Rains (rains(AT)caltech.edu)
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