Problema 25

Problema:

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?

Solución:

/*
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 * and open the template in the editor.
 */
package projecteuler;

import java.math.BigInteger;

/**
 *
 * @author lyonn
 */
public class C25 {

    public void resultado() {

        int i = 1;
        BigInteger[] fx = new BigInteger[50000];
        fx[0] = BigInteger.valueOf(1);
        fx[1] = BigInteger.valueOf(1);

        int tmp = 2;

        for (i = 1; i <= 10000; i++) {

            //fx[tmp]+=BigInteger.valueOf(fx[i-1]+fx[i]);
            fx[tmp] = fx[i].add(fx[i - 1]);
           
            tmp++;

        }
       
        for (i=0; i<=tmp-2; i++) {
             //System.out.println("F" + (i+1) + ": " + fx[i] +" Length:"+ fx[i].toString().length());
             if (fx[i].toString().length() == 1000) {
                 System.out.println("F" + (i+1) + ": " + fx[i] +" Length:"+ fx[i].toString().length());
                 break;
             }
                
            
        }
       

    }

}