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A lagged Fibonacci sequence
Problem 258
Published on Saturday, 3rd October 2009, 09:00 am; Solved by 1282;
Difficulty rating: 70%
A sequence is defined as:
g
_{k}
= 1, for 0 ≤
k
≤ 1999
g
_{k}
=
g
_{k-2000}
+
g
_{k-1999}
, for
k
≥ 2000.
Find
g
_{k}
mod 20092010 for
k
= 10
^{18}
.