[seqfan] No loop in view?

[Éric Angelini]

Hello SeqFans,
while I was searching my old messy papers to answer a request
from Alex Bellos, I've bumped into this idea yesterday:

"The chunks sizes of consonants squeezed between successive
 pairs of vowels are given by the sequence itself":

ONE, TWO, THREE, ZERO, ONE, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ...

The sequence obviously extends itself forever -- but does it
enter in a loop at some point?

Jean-Marc Falcoz has computed 30,000 terms and found no loop
(a third of the terms are 0s, two thirds are 1s). Does someone
have an idea about the sequence entering at some point in a 
loop -- or never?
Best,
É.
[a copy of this mail was sent to Jean-Marc Falcoz and Neil Sloane]