A003644 Discriminants of the known imaginary quadratic fields with 1 class per genus (a finite sequence). (Formerly M2333)

3, 4, 7, 8, 11, 15, 19, 20, 24, 35, 40, 43, 51, 52, 67, 84, 88, 91, 115, 120, 123, 132, 148, 163, 168, 187, 195, 228, 232, 235, 267, 280, 312, 340, 372, 403, 408, 420, 427, 435, 483, 520, 532, 555, 595, 627, 660, 708, 715, 760, 795, 840, 1012, 1092, 1155, 1320, 1380, 1428, 1435, 1540, 1848, 1995, 3003, 3315, 5460

Offset

1,1

Comments

This is the complete table from Borevich and Shafarevich.

If the GRH is true, the list contains the discriminants of all imaginary quadratic fields with 1 class per genus; otherwise, there may be one more such discriminant not on the list. (See Weinberger.) - Everett W. Howe, Aug 01 2014

References

Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 425-430.

L. E. Dickson, Introduction to the Theory of Numbers. Dover, NY, 1957, p. 85.

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..65.

Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.

P. J. Weinberger, Exponents of the class groups of complex quadratic fields, Acta Arith. 22 (1973), 117-124.

Prog

(PARI) ok(n)={isfundamental(-n) && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ Andrew Howroyd, Jul 20 2018

Crossrefs

Cf. A133288, A316743.

Sequence in context: A050122 A179016 A003657 * A196923 A192051 A033195

Adjacent sequences: A003641 A003642 A003643 * A003645 A003646 A003647

Keyword

nonn,fini,full,nice

Author

N. J. A. Sloane, Mira Bernstein

Extensions

Clarified name (added "the known") - Everett W. Howe, Aug 01 2014

Status

approved