project-euler

1000-digit Fibonacci number

Problem Description

The Fibonacci sequence is defined by the recurrence relation:

• F_n = F_n−1 + F_n−2, where F₁ = 1 and F₂ = 1.

Hence the first 12 terms will be:

• F₁ = 1
• F₂ = 1
• F₃ = 2
• F₄ = 3
• F₅ = 5
• F₆ = 8
• F₇ = 13
• F₈ = 21
• F₉ = 34
• F₁₀ = 55
• F₁₁ = 89
• F₁₂ = 144

The 12th term, F₁₂, is the first term to contain three digits.

What is the index of the first term in the Fibonacci sequence to contain 1000 digits?

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