_{This problem is a programming version of Problem 186 from projecteuler.net}

Here are the records from a busy telephone system with one million users:

The telephone number of the caller and the called number in record are and where come from the "Lagged Fibonacci Generator":

For ,
For ,

If = then the user is assumed to have misdialled and the call fails; otherwise the call is successful.

From the start of the records, we say that any pair of users and are friends if calls or vice-versa. Similarly, is a friend of a friend of if is a friend of and is a friend of ; and so on for longer chains.

The Prime Minister's phone number is . After how many successful calls, not counting misdials, will % of the users (including the PM) be a friend, or a friend of a friend etc., of the Prime Minister?