# What Would You Call A Non-base 10 Decimal?

Let $$a_k$$ represent the repeating decimal $$0.\overline{133}_k$$ for $$k \geq 4$$. The product $$a_4 a_5 \cdots a_{99}$$ can be expressed as $$\frac{m}{n!}$$ where $$m, n$$ are positive integers and $$n$$ is as small as possible. $$\frac{m}{n}$$ can be expressed as $$\frac{p}{q}$$ where $$p, q$$ are coprime integers. What is $$p+q$$?

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