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A005847 Imaginary quadratic fields with class number 2 (a finite sequence).
(Formerly M3749)
9

%I M3749 #28 Oct 21 2020 03:45:03

%S 5,6,10,13,15,22,35,37,51,58,91,115,123,187,235,267,403,427

%N Imaginary quadratic fields with class number 2 (a finite sequence).

%C n such that Q(sqrt(-n)) has class number 2.

%C The PARI code lists the imaginary quadratic fields Q(sqrt(-d)) with small class number and produces A003173 (class number 1), A005847 (2), A006203 (3).

%D 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 P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 142.

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

%H Steven Arno, M. L. Robinson, Ferrell S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arith. 83 (1998), pp. 295-330.

%H David Masser, <a href="https://arxiv.org/abs/2010.10256">Alan Baker</a>, arXiv:2010.10256 [math.HO], 2020. See p. 24.

%H Keith Matthews, <a href="http://www.numbertheory.org/classnos/">Tables of imaginary quadratic fields with small class numbers</a>.

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%t Select[Range[200], MoebiusMu[#] != 0 && NumberFieldClassNumber[Sqrt[-#]] == 2 &] (* _Alonso del Arte_, May 28 2015 *)

%o (PARI) { bnd = 10000; S = vector(10,X,[]); for (i = 1, bnd, if (issquarefree(i), n = qfbclassno(if(i%4==3,-i,-4*i)); if (n<11, S[n] = concat(S[n],i), ), )); } \\ Robert Harley (Robert.Harley(AT)inria.fr)

%K nonn,fini,full

%O 1,1

%A _N. J. A. Sloane_.

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Last modified March 28 13:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)