# Problem 186: Connectedness of a network
Here are the records from a busy telephone system with one million
users: RecNrCallerCalled120000710005326001835004393600863701497.........
The telephone number of the caller and the called number in record n are
Caller(n) = S2n-1 and Called(n) = S2n where S1,2,3,... come from the
"Lagged Fibonacci Generator": For 1 ≤ k ≤ 55, Sk = \[100003 - 200003k +
300007k3\] (modulo 1000000) For 56 ≤ k, Sk = \[Sk-24 + Sk-55\] (modulo
1000000) If Caller(n) = Called(n) 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 X and Y are
friends if X calls Y or vice-versa. Similarly, X is a friend of a friend
of Z if X is a friend of Y and Y is a friend of Z; and so on for longer
chains. The Prime Minister's phone number is 524287. After how many
successful calls, not counting misdials, will 99% of the users
(including the PM) be a friend, or a friend of a friend etc., of the
Prime Minister?