One thing that sets PEAC apart from the Fibonacci and Pisano series is the parity, or mod 2 remainder.

When you take the natural sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597...

The mod 2 is 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, ...

But since PEAC uses all the state space, by definition there must be (almost) as many odd and even numbers. So the 0, 1, 1 sequence can not repeat infinitely.

That's something to measure soon...