Web Reference: When I first did this problem I did not have my ultra fast Fibonacci number generator, so I will explain how to do it with the regular Fibonacci number generator. What is the first term in the Fibonacci sequence to contain 1000 digits? I made a brute force solution in Python but it takes forever. Can anyone suggest a non brute force solution? if NthTerm == 1 or NthTerm == 2: What is the index of the first term in the Fibonacci sequence to contain 1000 digits? Python's unbounded ints again make this trivial — but we can make it even easier! implies that F n very quickly converges to 1 5 φ n, where φ = 1 + 5 2. We thus need to find the smallest n such that 1 5 φ n ≥ 10 999.
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