

A003171


Negated discriminants of orders of imaginary quadratic fields with 1 class per genus (a finite sequence).
(Formerly M2331 N0922)


5



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
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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. 425430.
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


PROG

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


CROSSREFS

Cf. A000926, A133288.
The fundamental terms are given in A003644.
Sequence in context: A154708 A227148 A026444 * A028970 A309388 A188259
Adjacent sequences: A003168 A003169 A003170 * A003172 A003173 A003174


KEYWORD

nonn,fini


AUTHOR

N. J. A. Sloane, Mira Bernstein


EXTENSIONS

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


STATUS

approved



