2.2 KiB
2.2 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f3851000cf542c50fe98 | 5 | Problem 25: 1000-digit Fibonacci number | 301897 |
Description
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 n
digits?
Instructions
Tests
tests:
- text: <code>digitFibonacci(5)</code> should return a number.
testString: assert(typeof digitFibonacci(5) === 'number');
- text: <code>digitFibonacci(5)</code> should return 21.
testString: assert.strictEqual(digitFibonacci(5), 21);
- text: <code>digitFibonacci(10)</code> should return 45.
testString: assert.strictEqual(digitFibonacci(10), 45);
- text: <code>digitFibonacci(15)</code> should return 69.
testString: assert.strictEqual(digitFibonacci(15), 69);
- text: <code>digitFibonacci(20)</code> should return 93.
testString: assert.strictEqual(digitFibonacci(20), 93);
Challenge Seed
function digitFibonacci(n) {
return n;
}
digitFibonacci(20);
Solution
const digitFibonacci = (n) => {
const digits = (num) => {
return num.toString().length;
};
let f1 = 1;
let f2 = 1;
let index = 3;
while (true) {
let fn = f1 + f2;
if (digits(fn) === n) return index;
[f1, f2] = [f2, fn];
index++;
}
};