  Let PG be the Proth-Gilbreath operator that transforms a sequence of integers
into the sequence of the absolute values of the differences between all pairs
of neighbor terms. Consider the infinite tables obtained by successive
iterations of PG applied to different initial sequences of integers. We study
these tables of higher order differences and characterize those that have
near-periodic features. As a biproduct, we also obtain two results on a class
of formal power series over the field with two elements F2 that can be
expressed as rational functions in several ways.
