A006203 Discriminants of imaginary quadratic fields with class number 3 (negated). (Formerly M5131)

23, 31, 59, 83, 107, 139, 211, 283, 307, 331, 379, 499, 547, 643, 883, 907

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

Table of n, a(n) for n=1..16.

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.

Index entries for sequences related to quadratic fields

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

Cf. A005847, A013658, A014602, A014603, A046002, ..., A046020.

Cf. also A003173, A005847, ...

Cf. A191410.

Sequence in context: A030670 A030680 A330162 * A153635 A052160 A165985

Adjacent sequences: A006200 A006201 A006202 * A006204 A006205 A006206

Keyword

fini,nonn,full,nice

Author

N. J. A. Sloane

Status

approved