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id	title	challengeType	forumTopicId	dashedName
5900f3851000cf542c50fe98	Problem 25: 1000-digit Fibonacci number	5	301897	problem-25-1000-digit-fibonacci-number

--description--

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 n digits?

--hints--

digitFibonacci(5) should return a number.

assert(typeof digitFibonacci(5) === 'number');

digitFibonacci(5) should return 21.

assert.strictEqual(digitFibonacci(5), 21);

digitFibonacci(10) should return 45.

assert.strictEqual(digitFibonacci(10), 45);

digitFibonacci(15) should return 69.

assert.strictEqual(digitFibonacci(15), 69);

digitFibonacci(20) should return 93.

assert.strictEqual(digitFibonacci(20), 93);

--seed--

--seed-contents--

function digitFibonacci(n) {

  return n;
}

digitFibonacci(20);

--solutions--

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++;
  }
};

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