

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
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OFFSET

2,2


COMMENTS

Let D be the nth 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.


REFERENCES

Sved, Marta. "Units in pure cubic number fields." Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 13 (1970), 141149.


LINKS

Table of n, a(n) for n=2..32.


CROSSREFS

Cf. A004709, A262562, A262563.
Sequence in context: A257696 A110730 A198339 * A264990 A277315 A277326
Adjacent sequences: A262558 A262559 A262560 * A262562 A262563 A262564


KEYWORD

sign,more


AUTHOR

N. J. A. Sloane, Oct 18 2015


STATUS

approved



