A005847 Imaginary quadratic fields with class number 2 (a finite sequence).

5, 6, 10, 13, 15, 22, 35, 37, 51, 58, 91, 115, 123, 187, 235, 267, 403, 427

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

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. 221-242 of "Number Theory, Carbondale 1979", Lect. Notes Math. 751 (1982).
• Paulo Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 142.
• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 143-144.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Steven Arno, M. L. Robinson, and Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998), pp. 295-330.
• David Masser, Alan Baker, arXiv:2010.10256 [math.HO], 2020. See p. 24.
• Keith Matthews, Tables of imaginary quadratic fields with small class numbers.
• Index entries for sequences related to quadratic fields.

Crossrefs

Cf. A003173, A005847, A006203.

Programs

Mathematica

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

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)