# Is this even a pattern?

Let $$S_{1}$$ represent $$1^{2+3}$$ and $$S_{2}$$ represent $$2^{3+4}$$ and this continues to the infinity. Given that $$a_{1}$$ is the digit sum of $$S_{999}$$ and $$a_{2}$$ is the digit sum of $$a_{1}$$ and so on and so forth, find the value of $$a_{99999999}$$

Note

This question is based on a popular number theory question.

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