Abstract
This research proposal is an introduction to ergodic theory focusing on its applications to number theory. More specifically, it consists in studying the stochastic behaviour of the following sequences of integers {1,2,4,8,1,3,6,1,2,5,1,...}(obtained taking the first digits of {2^n} and the sequence of the digits of the decimal expansion of a real number. In this way, the project lies div…