A262561 The x coordinate of the fundamental unit in the cubic field Q(D^(1/3)): see Comments for precise definition.

-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

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

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

Marta Sved, Units in pure cubic number fields, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 13 (1970), 141-149.

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