Project Euler – Problem 25 Solution

Problem

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 first term in the Fibonacci sequence to contain 1000 digits?

Solution

let fibonacciSeq =
    Seq.unfold (fun (current, next) -> Some(current, (next, current + next))) (0I, 1I)
    |> Seq.filter (fun f -> f > 0I)

let answer = (Seq.findIndex (fun f -> f.ToString().Length >= 1000) fibonacciSeq) + 1

In my solution here I first created a Fibonacci sequence which starts with 1, 1, … all the way to infinity, and the second expression gives us the answer to the problem by using Seq.findIndex to find the index (zero-based) of the first element which contains 1000 digits. The ‘+ 1’ at the end simply converts the zero-based index to the one-based index which the problem is asking for.