added Problem 25

Author: byt3h3ad

Project-Euler/Problem025.js

@@ -0,0 +1,59 @@
+/**
+* Problem 20 - 1000-digit Fibonacci number
+*
+* @see {@link https://projecteuler.net/problem=25}
+*
+* The Fibonacci sequence is defined by the recurrence relation:
+* 
+* Fn = Fn−1 + Fn−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?
+*/
+
+// brute force method
+
+function fibonacci(n) {
+  // Creates an array of Fibonacci numbers using the Fibonacci formula. Returns the nth element of the array.
+  if (n === 1) {
+    return 0
+  }
+  else if (n === 2) {
+    return 1
+  }
+  else {
+    series = [0,1]
+    for (let i = 2; i <= n; i++) {
+      series.push(sequence[i-1]+sequence[i-2])
+    }
+    return sequence[n]
+  }
+}
+
+function fibonacciIndex(n = 1000) {
+  // Computes incrementing Fibonacci numbers starting from 3 and checks if its length is equal to n. Returns the term of the sequence in which it happens first.
+  let digits = 0
+  let index = 2
+  while (digits < n) {
+    index += 1
+    digits = fibonacci(index).toString().length
+  }
+  return index
+}
+
+export { fibonacciIndex }