If \( \displaystyle \sum_{r=1}^\infty \dfrac r{r^4+r^2+1} = 1 - \dfrac1a \), find the number of digits in \(a^{2016} \).

You are given the following approximations: \(\log 10 = 1, \log 5 = 0.6990, \log 3 = 0.4771 \).

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