Avoiding Three Consecutive Blocks of the Same Size and Same Sum
  We show that there exists an infinite word over the alphabet {0, 1, 3, 4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from 1994. 
Julien Cassaigne, James D. Currie, Luke Schaeffer, Jeffrey Shallit
cs.DM math.CO