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823,543 The pattern is n to the nth power.
512 squared
8
46656 as it is 6 to the power of 6. Each in turn is the result of a number to the power of itself.
Oh, what a happy little sequence we have here! It looks like we're doubling every other number. So, after 16, the next number would be 16 doubled, which is 32. Just like painting a beautiful landscape, sometimes patterns can be found in the most unexpected places.