  We define an algorithm which begins with an sequence of sequences, and
produces a single sequence, with following property: If at least one of the
original sequences has a tail that is periodic, then the output sequence has a
periodic tail, and conversely. Our purpose is to supplement a result by
Dasaratha et al., in which a real number input results in a countable family of
sequences, with the property that at least one is eventually periodic if and
only if the input is a cubic irrational number. This result, in the context of
that one, attempts to address Hermite's problem, which asks for some
generalization of continued fractions that can detect cubic numbers via
periodicity. We note in our ending remarks how this particular trick fails to
give a satisfying resolution to Hermite's problem, but we present it anyway,
for anyone whom it may interest.

Combinatorics