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A lagged Fibonacci sequence

Problem 258

Published on Saturday, 3rd October 2009, 09:00 am; Solved by 884

A sequence is defined as:

  • gk = 1, for 0 ≤ k ≤ 1999
  • gk = gk-2000 + gk-1999, for k ≥ 2000.

Find gk mod 20092010 for k = 1018.