A262563 The z coordinate of the fundamental unit in the cubic field Q(D^(1/3)): see Comments for precise definition.

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

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, A262561, A262562.

Sequence in context: A160018 A175099 A151867 * A170843 A362961 A292596

Adjacent sequences: A262560 A262561 A262562 * A262564 A262565 A262566

Keyword

sign,more

Author

N. J. A. Sloane, Oct 18 2015

Status

approved