A003171 Negated discriminants of orders of imaginary quadratic fields with 1 class per genus (a finite sequence).

3, 4, 7, 8, 11, 12, 15, 16, 19, 20, 24, 27, 28, 32, 35, 36, 40, 43, 48, 51, 52, 60, 64, 67, 72, 75, 84, 88, 91, 96, 99, 100, 112, 115, 120, 123, 132, 147, 148, 160, 163, 168, 180, 187, 192, 195, 228, 232, 235, 240, 267, 280, 288, 312, 315, 340, 352, 372, 403

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• fini

Comments

It is conjectured that a(101) = 7392 is the last term. If it would exist, a(102) > 10^6. - Hugo Pfoertner, Dec 01 2019

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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..101
• Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
• Jianing Song, List of the corresponding class groups

Crossrefs

Cf. A000926, A133288.

The fundamental terms are given in A003644.

Programs

PARI

ok(n)={(-n)%4<2 && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ Andrew Howroyd, Jul 20 2018

Extensions

Terms a(44) and beyond from Andrew Howroyd, Jul 20 2018