yaworsw/euler-manager

---
:id: 323
:name: Bitwise-OR operations on random integers
:url: https://projecteuler.net/problem=323
:content: "Let <var>y</var><sub>0</sub>, <var>y</var><sub>1</sub>, <var>y</var><sub>2</sub>,...
  be a sequence of random unsigned 32 bit integers  \n(i.e. 0 ≤ <var>y<sub>i</sub></var>
  \\< 2<sup>32</sup>, every value equally likely).\n\nFor the sequence <var>x<sub>i</sub></var>
  the following recursion is given:\n\n- <var>x</var><sub>0</sub> = 0 and\n- <var>x<sub>i</sub></var>
  = <var>x</var><sub><var>i</var>-<i>1</i></sub> **|** <var>y</var><sub><var>i</var>-<i>1</i></sub>,
  for <var>i</var> \\> 0. ( **|** is the bitwise-OR operator)\n\nIt can be seen that
  eventually there will be an index N such that <var>x<sub>i</sub></var> = 2<sup>32</sup>
  -1 (a bit-pattern of all ones) for all <var>i</var> ≥ N.\n\nFind the expected value
  of N.   \nGive your answer rounded to 10 digits after the decimal point.\n\n"