Math Help -> Puzzles -> Nondecreasing integer sequence 2 

Let a₁,a₂,...,a₂₀₀₅ be a nondecreasing sequence of positive integers, with t defined as t=a₂₀₀₅.
Let b_n be the smallest index, m, for which a_m ≥ n.
In terms of t, what is the smallest possible value of the sum a₁+a₂+...+a₂₀₀₅+b₁+b₂+...+b_t ?