# Find the remainder

Number Theory Level pending

Let $$n_1$$, $$n_2$$, $$n_3$$, $$\ldots$$ be the increasing sequence of natural numbers each of which leaves remainder $$r$$ when it is divided by $$r+1$$ for $$r = 2,3,4,\ldots,9$$. What is the remainder when $$n_{2008}$$ is divided by 11?

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