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A005847 Imaginary quadratic fields with class number 2 (a finite sequence).
(Formerly M3749)
9
5, 6, 10, 13, 15, 22, 35, 37, 51, 58, 91, 115, 123, 187, 235, 267, 403, 427 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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)

REFERENCES

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).

LINKS

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

PROG

(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), ), )); }

CROSSREFS

Sequence in context: A062845 A236307 A166563 * A109758 A015820 A096728

Adjacent sequences:  A005844 A005845 A005846 * A005848 A005849 A005850

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 22 17:45 EST 2014. Contains 252365 sequences.