2021-12-10 11:14:24 +05:30
|
|
|
|
---
|
|
|
|
|
|
id: 5900f5271000cf542c51003a
|
|
|
|
|
|
title: 'Завдання 443: Послідовність НСД'
|
|
|
|
|
|
challengeType: 5
|
|
|
|
|
|
forumTopicId: 302115
|
|
|
|
|
|
dashedName: problem-443-gcd-sequence
|
|
|
|
|
|
---
|
|
|
|
|
|
|
|
|
|
|
|
# --description--
|
|
|
|
|
|
|
|
|
|
|
|
Нехай $g(n)$ — це послідовність, яка визначається так:
|
|
|
|
|
|
|
2022-04-11 19:34:39 +05:30
|
|
|
|
$$\begin{align} & g(4) = 13, \\\\
|
|
|
|
|
|
& g(n) = g(n-1) + gcd(n, g(n - 1)) \text{ for } n > 4. \end{align}$$
|
2021-12-10 11:14:24 +05:30
|
|
|
|
|
|
|
|
|
|
Перші кілька значень:
|
|
|
|
|
|
|
2022-04-11 19:34:39 +05:30
|
|
|
|
$$\begin{array}{l} n & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & \ldots \\\\
|
|
|
|
|
|
g(n) & 13 & 14 & 16 & 17 & 18 & 27 & 28 & 29 & 30 & 31 & 32 & 33 & 34 & 51 & 54 & 55 & 60 & \ldots \end{array}$$
|
2021-12-10 11:14:24 +05:30
|
|
|
|
|
|
|
|
|
|
Дано, що $g(1\\,000) = 2\\,524$, а $g(1\\,000\\,000) = 2\\,624\\,152$.
|
|
|
|
|
|
|
|
|
|
|
|
Знайдіть $g({10}^{15})$.
|
|
|
|
|
|
|
|
|
|
|
|
# --hints--
|
|
|
|
|
|
|
|
|
|
|
|
`gcdSequence()` має видати `2744233049300770`.
|
|
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
|
assert.strictEqual(gcdSequence(), 2744233049300770);
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
# --seed--
|
|
|
|
|
|
|
|
|
|
|
|
## --seed-contents--
|
|
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
|
function gcdSequence() {
|
|
|
|
|
|
|
|
|
|
|
|
return true;
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
gcdSequence();
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
# --solutions--
|
|
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
|
// solution required
|
|
|
|
|
|
```
|
