86 lines
1.9 KiB
Markdown
86 lines
1.9 KiB
Markdown
---
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id: 5900f3851000cf542c50fe98
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title: 'Problem 25: 1000-digit Fibonacci number'
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challengeType: 5
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forumTopicId: 301897
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dashedName: problem-25-1000-digit-fibonacci-number
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---
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# --description--
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The Fibonacci sequence is defined by the recurrence relation:
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<div style='padding-left: 4em;'>F<sub>n</sub> = F<sub>n−1</sub> + F<sub>n−2</sub>, where F<sub>1</sub> = 1 and F<sub>2</sub> = 1.</div>
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Hence the first 12 terms will be:
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<div style='padding-left: 4em; display: inline-grid; grid-template-rows: auto; row-gap: 7px;'><div>F<sub>1</sub> = 1</div><div>F<sub>2</sub> = 1</div><div>F<sub>3</sub> = 2</div><div>F<sub>4</sub> = 3</div><div>F<sub>5</sub> = 5</div><div>F<sub>6</sub> = 8</div><div>F<sub>7</sub> = 13</div><div>F<sub>8</sub> = 21</div><div>F<sub>9</sub> = 34</div><div>F<sub>10</sub> = 55</div><div>F<sub>11</sub> = 89</div><div>F<sub>12</sub> = 144</div></div>
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The 12th term, F<sub>12</sub>, is the first term to contain three digits.
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What is the index of the first term in the Fibonacci sequence to contain `n` digits?
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# --hints--
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`digitFibonacci(5)` should return a number.
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```js
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assert(typeof digitFibonacci(5) === 'number');
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```
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`digitFibonacci(5)` should return 21.
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```js
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assert.strictEqual(digitFibonacci(5), 21);
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```
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`digitFibonacci(10)` should return 45.
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```js
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assert.strictEqual(digitFibonacci(10), 45);
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```
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`digitFibonacci(15)` should return 69.
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```js
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assert.strictEqual(digitFibonacci(15), 69);
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```
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`digitFibonacci(20)` should return 93.
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```js
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assert.strictEqual(digitFibonacci(20), 93);
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```
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# --seed--
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## --seed-contents--
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```js
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function digitFibonacci(n) {
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return n;
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}
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digitFibonacci(20);
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```
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# --solutions--
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```js
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const digitFibonacci = (n) => {
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const digits = (num) => {
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return num.toString().length;
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};
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let f1 = 1;
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let f2 = 1;
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let index = 3;
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while (true) {
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let fn = f1 + f2;
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if (digits(fn) === n) return index;
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[f1, f2] = [f2, fn];
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index++;
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}
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};
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```
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