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%I M5131 #45 May 16 2022 02:09:01
%S 23,31,59,83,107,139,211,283,307,331,379,499,547,643,883,907
%N Discriminants of imaginary quadratic fields with class number 3 (negated).
%C Also n such that Q(sqrt(-n)) has class number 3. Lubelski in 1936 proved that 907 is maximal term of this sequence. - _Artur Jasinski_, Oct 07 2011
%D H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 514.
%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 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 Kurt Heegner, <a href="http://dx.doi.org/10.1007/BF01174749">Diophantische Analysis und Modulfunktionen</a>, Matematische Zaitschrift, 1952, Vol. 56. p. 253.
%H S. Lubelski, <a href="https://doi.org/10.4064/aa-1-2-169-183">Zur Reduzibilität von Polynomen in Kongruenzentheorie</a>, Acta Arithmetica 1 (1935) pp. 169-183.
%H Keith Matthews, <a href="http://www.numbertheory.org/classnos/">Tables of imaginary quadratic fields with small class numbers</a>
%H Pieter Moree and Armand Noubissie, <a href="https://arxiv.org/abs/2205.06685">Higher Reciprocity Laws and Ternary Linear Recurrence Sequences</a>, arXiv:2205.06685 [math.NT], 2022. See p. 4.
%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[1000], NumberFieldClassNumber[ Sqrt[-#]] == 3 & ]] (* _Jean-François Alcover_, Jan 04 2012 *)
%o (PARI) ok(n)={isfundamental(-n) && quadclassunit(-n).no == 3} \\ _Andrew Howroyd_, Jul 20 2018
%o (Sage) [n for n in (1..1000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==3] # _G. C. Greubel_, Mar 01 2019
%Y Cf. A005847, A013658, A014602, A014603, A046002, ..., A046020.
%Y Cf. also A003173, A005847, ...
%Y Cf. A191410.
%K fini,nonn,full,nice
%O 1,1
%A _N. J. A. Sloane_