Problem 323: Bitwise-OR operations on random integers

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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.