

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
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OFFSET

1,1


COMMENTS

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).


REFERENCES

J. M. Masley, Where are the number fields with small class number?, pp. 221242 of "Number Theory, Carbondale 1979", Lect. Notes Math. 751 (1982).
P. Ribenboim, The Book of Prime Number Records. SpringerVerlag, 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.
Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998), pp. 295330.
Keith Matthews, Tables of imaginary quadratic fields with small class numbers.
Index entries for sequences related to quadratic fields


MATHEMATICA

Select[Range[200], MoebiusMu[#] != 0 && NumberFieldClassNumber[Sqrt[#]] == 2 &] (* Alonso del Arte, May 28 2015 *)


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), ), )); } \\ Robert Harley (Robert.Harley(AT)inria.fr)


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



