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A006832
Discriminants of totally real cubic fields.
(Formerly M5296)
20
49, 81, 148, 169, 229, 257, 316, 321, 361, 404, 469, 473, 564, 568, 621, 697, 733, 756, 761, 785, 788, 837, 892, 940, 961, 985, 993, 1016, 1076, 1101, 1129, 1229, 1257, 1300, 1304, 1345, 1369, 1373, 1384, 1396, 1425, 1436, 1489, 1492, 1509, 1524
OFFSET
1,1
REFERENCES
Pohst and Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, page 436.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Robin Visser, Table of n, a(n) for n = 1..10000 (terms n = 1..130 from R. J. Mathar).
K. Belabas, A fast algorithm to compute cubic fields, Math. Comp. 66 (1997), no. 219, 1213-1237.
T. W. Cusick and L. Schoenfeld, A table of fundamental pairs of units in totally real cubic fields, Math. Comp. 48 (1987), 147-158.
V. Ennola and R. Turunen, On totally real cubic fields, Math. Comp. 44 (1985), no. 170, 495-518.
P. Llorente and J. Quer, On totally real cubic fields with discriminant D < 10^7, Math. Comp. 50 (1988), no. 182, 581-594.
EXAMPLE
The field Q[x]/(x^3 - x^2 - 2*x + 1) is the totally real cubic field with the smallest discriminant of 49. - Robin Visser, Apr 17 2025
CROSSREFS
Sequence in context: A207638 A286095 A106311 * A343000 A343022 A250074
KEYWORD
nonn
STATUS
approved