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Let aka_kak denote the number of digits in 2k2^k2k. For instance, since 24=162^4 = 1624=16, we have a4=2a_4 = 2a4=2.
Compute the limit
limn→∞1n2∑k=1nak.\lim_{n\to\infty} \frac{1}{n^2} \sum_{k=1}^{n} a_k. n→∞limn21k=1∑nak.
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