The "interpolating polynomial" method may not work since it can produce infinite solutions if you lift the orders of the polynomial functions. In Wolfram Alpha, if we input random 8th and 9th items, we can fit the sequence into another function.

The basic tricks of guessing the sequence number seem not working due to the 0s in the numbers. It does roughly look like an exponential curve in its trend, by looking at the graph. So it may look familiar as the growth of total-number-of-websites from 1990s, etc., but I didn't find the exactly matched numbers from sources like Steem witness, Bitcoin nodes, etc.

The intention of the author is the important key to get the "right" answer. With some hints in the question ("a unique competition"), it can be a good attempt to expect there're more context and meanings (e.g. mapping to some words) besides a pure numerical game. However, I'm sorry I didn't catch enough information with limited investigation. As long as I cannot read the minds of the author, I can only provide the rough guess based on the sequence itself.

Since the 900 in the sequence looks suspicious, I'm splitting the sequence into two, and some guess / fitting / prediction accordingly.

My guess is (9300, 57000)