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A005847
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Imaginary quadratic fields with class number 2 (a finite sequence).
(Formerly M3749)
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9
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5, 6, 10, 13, 15, 22, 35, 37, 51, 58, 91, 115, 123, 187, 235, 267, 403, 427
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OFFSET
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1,1
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COMMENTS
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n such that Q(sqrt(-n)) has class number 2.
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).
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REFERENCES
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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).
P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 142.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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David Masser, Alan Baker, arXiv:2010.10256 [math.HO], 2020. See p. 24.
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MATHEMATICA
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Select[Range[200], MoebiusMu[#] != 0 && NumberFieldClassNumber[Sqrt[-#]] == 2 &] (* Alonso del Arte, May 28 2015 *)
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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