CONO-SUR 2006 Problem 3

Let $n$ be a natural number. The finite sequence $\alpha$ of positive integer terms, there are $n$ different numbers ( $\alpha$ can have repeated terms). Moreover, if from one from its terms any we subtract 1, we obtain a sequence which has, between its terms, at least $n$ different positive numbers. What's the minimum value of the sum of all the terms of $\alpha$ ?