id	title	challengeType	forumTopicId	dashedName
5900f4b01000cf542c50ffc2	Problem 323: Bitwise-OR operations on random integers	5	301980	problem-323-bitwise-or-operations-on-random-integers

--description--

Let y_0, y_1, y_2, \ldots 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:

x_0 = 0 and
x_i = x_{i - 1} \mathbf{|} y_{i - 1}, for i > 0. (\mathbf{|} is the bitwise-OR operator)

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.

--hints--

bitwiseOrOnRandomIntegers() should return 6.3551758451.

assert.strictEqual(bitwiseOrOnRandomIntegers(), 6.3551758451);

function bitwiseOrOnRandomIntegers() {

  return true;
}

bitwiseOrOnRandomIntegers();

// solution required