  Reduced ideals have been defined in the context of integer rings in quadratic
number fields, and they are closely tied to the continued fraction algorithm.
The notion of this type of ideal extends naturally to number fields of higher
degree. In the case of pure cubic fields, generated by cube roots of integers,
a convenient integral basis provides a means for identifying reduced ideals in
these fields. We define integer sequences whose terms are in correspondence
with some of these ideals, suggesting a generalization of continued fractions.
