  Given a finite word u, we define its palindromic length |u|_{pal} to be the
least number n such that u=v_1v_2... v_n with each v_i a palindrome. We address
the following open question: Does there exist an infinite non ultimately
periodic word w and a positive integer P such that |u|_{pal}<P for each factor
u of w? We give a partial answer to this question by proving that if an
infinite word w satisfies the so-called (k,l)-condition for some k and l, then
for each positive integer P there exists a factor u of w whose palindromic
length |u|_{pal}>P. In particular, the result holds for all the k-power-free
words and for the Sierpinski word.
