## Bitwise-OR operations on random integers

### Problem 323

Published on Sunday, 6th February 2011, 07:00 am; Solved by 1430

Let y0, y1, y2,... be a sequence of random unsigned 32 bit integers
(i.e. 0 yi 232, every value equally likely).

For the sequence xi the following recursion is given:

- x0 = 0 and
- xi = xi-1 | yi-1, for i 0. ( | is the bitwise-OR operator)

It can be seen that eventually there will be an index N such that xi = 232 -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.