Let y_{0}, y_{1}, y_{2},... be a sequence of random unsigned 32 bit integers
(i.e. 0 y_{i} 2^{32}, every value equally likely).
For the sequence x_{i} the following recursion is given:
It can be seen that eventually there will be an index N such that x_{i} = 2^{32} -1 (a bit-pattern of all ones) for all i N.
Find the expected value of N.
Give your answer rounded to 10 digits after the decimal point.
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK