|
|
A262561
|
|
The x coordinate of the fundamental unit in the cubic field Q(D^(1/3)): see Comments for precise definition.
|
|
3
|
|
|
-1, -2, -1, 1, 1, 2, -2, -3, 1, 1, -4, 1, 1, 18, 1, 1, 1, -47, 23, -41399, 1, 3, 0, -322461439, 1, -367, 3742201, 613, -7, 1, 10
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,2
|
|
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|