Forbidden number in Fibonacci

Let \(F_n = F_{n-1}+ F_{n-2}\) be the \(n^\text{th}\) Fibonacci number \((n>0)\), where \(F_1=1\) and \(F_2=1\).

If we consider the last 3 digits of the Fibonacci numbers, not all numbers from 0 to 999 appear in the sequence.

\(\quad \) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 597, 584, 181, ...

What is the largest integer from 0 to 999 that doesn't appear in this sequence?


Inspiration.

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