Adamczewski Boris & Yann Bugeaud
Real and $p$adic expansions involving symmetric patterns
This paper is motivated by the nonArchimedean counterpart of a problem raised by Mahler and Mendès France, and by questions related to the expected normality of irrational algebraic numbers. We introduce a class of sequence enjoying a particular combinatorial property: the precocious occurrences of infinitely many symmetric patterns. Then, we prove some transcendence statements involving both real and $p$adic numbers associated with such palindromic sequences.
