1.1 KiB
1.1 KiB
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4c11000cf542c50ffd3 | Problem 341: Golomb's self-describing sequence | 5 | 302000 | problem-341-golombs-self-describing-sequence |
--description--
The Golomb's self-describing sequence (G(n)) is the only nondecreasing sequence of natural numbers such that n appears exactly G(n) times in the sequence. The values of G(n) for the first few n are
\begin{array}{c}
n & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & \ldots \\\\
G(n) & 1 & 2 & 2 & 3 & 3 & 4 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 6 & 6 & \ldots
\end{array}$$
You are given that $G({10}^3) = 86$, $G({10}^6) = 6137$.
You are also given that $\sum G(n^3) = 153\\,506\\,976$ for $1 ≤ n < {10}^3$.
Find $\sum G(n^3)$ for $1 ≤ n < {10}^6$.
# --hints--
`golombsSequence()` should return `56098610614277016`.
```js
assert.strictEqual(golombsSequence(), 56098610614277016);
```
# --seed--
## --seed-contents--
```js
function golombsSequence() {
return true;
}
golombsSequence();
```
# --solutions--
```js
// solution required
```