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A262563
The z coordinate of the fundamental unit in the cubic field Q(D^(1/3)): see Comments for precise definition.
3
0, 1, 1, 2, 3, 0, 0, 2, -2, -3, 2, -1, 12, 0, 3, -1, -1, 4, -4, 6230, -4, 0, 1, 370284, -3, 20, -394098, -51, -1, -6, 0
OFFSET
2,4
COMMENTS
Let D be the n-th cubefree number greater than 1, that is, D = A004709(n), n >= 2.
Let F = cubic field Q(D^(1/3)). Let eta be the positive fundamental unit in F. Then eta has a unique representation as eta = x + y*alpha + z*gamma, where (1,alpha,gamma) is the appropriate modified Dedekind basis for F. Then x,y,z are given by A262561, A262562, A262563 respectively.
See Sved (1970) for further details. Sved gives a table for all D < 200.
LINKS
Marta Sved, Units in pure cubic number fields, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 13 (1970), 141-149.
CROSSREFS
KEYWORD
sign,more
AUTHOR
N. J. A. Sloane, Oct 18 2015
STATUS
approved