[go: up one dir, main page]

login
A003171
Negated discriminants of orders of imaginary quadratic fields with 1 class per genus (a finite sequence).
(Formerly M2331 N0922)
6
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
1,1
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
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
PROG
(PARI) ok(n)={(-n)%4<2 && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ Andrew Howroyd, Jul 20 2018
CROSSREFS
The fundamental terms are given in A003644.
Sequence in context: A154708 A227148 A026444 * A028970 A309388 A188259
KEYWORD
nonn,fini
EXTENSIONS
Terms a(44) and beyond from Andrew Howroyd, Jul 20 2018
STATUS
approved