  A strictly stationary sequence of random variables is constructed with the
following properties: (i) the random variables take the values -1 and +1 with
probability 1/2 each, (ii) every five of the random variables are independent,
(iii) the sequence is "causal" in a certain sense, (iv) the sequence has a
trivial double tail sigma-field, and (v) regardless of the normalization used,
the partial sums do not converge to a (nondegenerate) normal law. The example
has some features in common with a recent construction (for an arbitrary fixed
positive integer N), by Alexander Pruss and the author, of a strictly
stationary N-tuplewise independent counterexample to the central limit theorem.
