An Unlucky Number?

Algebra Level 4

n=02n132n+1 \large \displaystyle \sum_{n=0}^\infty \frac {2^n}{13^{2^n} + 1}

The closed form of the above summation is equals to pq\frac p q for coprime positive integers p,qp,q. What is the value of p+qp+ q?

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