  The notion of palindromic length of a finite word, as well as an infinite
word, was first introduced by Frid, Puzynina and Zamboni\cite{FRID2013737}.
They conjectured that if the palindromic length of an infinite word is bounded,
then this sequence is eventually periodic. In this article, we give a formal
expression of the palindromic length of Thue-Morse sequence and find all
sequences which have the same palindromic length as Thue-Morse's.
