Project Euler Problem 25

Problem 25

30 August 2002

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?

Answer: 4782

 

 

C#

 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;
using System.IO;

namespace Euler {
    class Program {
        static void Main(string[] args) {
            BigInteger f = 1;
            BigInteger a = 1;
            BigInteger b = 1;
            int i = 3;
            for (i = 3; ; i++) {
                f = a + b;
                a = b;
                b = f;
                if (f.ToString().Length >= 1000) break;                
            }
            Console.WriteLine(i);
            Console.ReadKey();
        }
    }
}

Racket

(let loop ([a 1]
           [b 1]
           [index 1])
  (if (>= (string-length (number->string a)) 1000)
      (displayln index)
      (loop b (+ a b) (add1 index))))