OFFSET
1,1
COMMENTS
Also n such that Q(sqrt(-n)) has class number 3. Lubelski in 1936 proved that 907 is maximal term of this sequence. - Artur Jasinski, Oct 07 2011
REFERENCES
H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 514.
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).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998), pp. 295-330.
Kurt Heegner, Diophantische Analysis und Modulfunktionen, Matematische Zaitschrift, 1952, Vol. 56. p. 253.
S. Lubelski, Zur Reduzibilität von Polynomen in Kongruenzentheorie, Acta Arithmetica 1 (1935) pp. 169-183.
Keith Matthews, Tables of imaginary quadratic fields with small class numbers
Pieter Moree and Armand Noubissie, Higher Reciprocity Laws and Ternary Linear Recurrence Sequences, arXiv:2205.06685 [math.NT], 2022. See p. 4.
Eric Weisstein's World of Mathematics, Class Number.
MATHEMATICA
Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] & ) /@ Select[ Range[1000], NumberFieldClassNumber[ Sqrt[-#]] == 3 & ]] (* Jean-François Alcover, Jan 04 2012 *)
PROG
(PARI) ok(n)={isfundamental(-n) && quadclassunit(-n).no == 3} \\ Andrew Howroyd, Jul 20 2018
(Sage) [n for n in (1..1000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==3] # G. C. Greubel, Mar 01 2019
CROSSREFS
KEYWORD
fini,nonn,full,nice
AUTHOR
STATUS
approved