Euler problem 25

The Fibonacci sequence is defined by the recurrence relation:

F_n = F_n1 + F_n2, 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 first term in the Fibonacci sequence to contain 1000 digits?

Solution:


The number of digits in F(n) is asymptotic to n*Log(Q) where Q = GoldenRatio = 1.61803;(see http://en.wikipedia.org/wiki/Fibonacci_number)

Problem25 =        4782 elapsed time:    0 ms. Test Passed.