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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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8
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5, 6, 10, 13, 15, 22, 35, 37, 51, 58, 91, 115, 123, 187, 235, 267, 403, 427
(list;
graph;
refs;
listen;
history;
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internal format)
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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 - from Robert Harley (Robert.Harley(AT)inria.fr) - 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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Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.
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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Table of n, a(n) for n=1..18.
Keith Matthews, Tables of imaginary quadratic fields with small class numbers.
Index entries for sequences related to quadratic fields
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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), ), )); }
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CROSSREFS
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Sequence in context: A102506 A062845 A166563 * A109758 A015820 A096728
Adjacent sequences: A005844 A005845 A005846 * A005848 A005849 A005850
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KEYWORD
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nonn,fini,full
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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