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A science communicator films a video on the Fibonacci sequence and its appearance in nature. She explains that the number of spirals in pinecones often follows Fibonacci numbers. If she models the spiral count as \( F_n = F_{n-1} + F_{n-2} \) with \( F_1 = 1, F_2 = 1 \), what is the smallest \( n \) such that \( F_n > 100 \)?
Compute Fibonacci numbers until exceeding 100:
\( F_1 = 1 \)

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