a9418a1fe9
* fix: clean-up Project Euler 221-240 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
62 lines
1.8 KiB
Markdown
62 lines
1.8 KiB
Markdown
---
|
|
id: 5900f45b1000cf542c50ff6d
|
|
title: 'Problem 238: Infinite string tour'
|
|
challengeType: 5
|
|
forumTopicId: 301883
|
|
dashedName: problem-238-infinite-string-tour
|
|
---
|
|
|
|
# --description--
|
|
|
|
Create a sequence of numbers using the "Blum Blum Shub" pseudo-random number generator:
|
|
|
|
$$
|
|
s_0 = 14025256 \\\\
|
|
s_{n + 1} = {s_n}^2 \\; mod \\; 20\\,300\\,713
|
|
$$
|
|
|
|
Concatenate these numbers $s_0s_1s_2\ldots$ to create a string $w$ of infinite length. Then, $w = 14025256741014958470038053646\ldots$
|
|
|
|
For a positive integer $k$, if no substring of $w$ exists with a sum of digits equal to $k$, $p(k)$ is defined to be zero. If at least one substring of $w$ exists with a sum of digits equal to $k$, we define $p(k) = z$, where $z$ is the starting position of the earliest such substring.
|
|
|
|
For instance:
|
|
|
|
The substrings 1, 14, 1402, … with respective sums of digits equal to 1, 5, 7, … start at position 1, hence $p(1) = p(5) = p(7) = \ldots = 1$.
|
|
|
|
The substrings 4, 402, 4025, … with respective sums of digits equal to 4, 6, 11, … start at position 2, hence $p(4) = p(6) = p(11) = \ldots = 2$.
|
|
|
|
The substrings 02, 0252, … with respective sums of digits equal to 2, 9, … start at position 3, hence $p(2) = p(9) = \ldots = 3$.
|
|
|
|
Note that substring 025 starting at position 3, has a sum of digits equal to 7, but there was an earlier substring (starting at position 1) with a sum of digits equal to 7, so $p(7) = 1$, not 3.
|
|
|
|
We can verify that, for $0 < k ≤ {10}^3$, $\sum p(k) = 4742$.
|
|
|
|
Find $\sum p(k)$, for $0 < k ≤ 2 \times {10}^{15}$.
|
|
|
|
# --hints--
|
|
|
|
`infiniteStringTour()` should return `9922545104535660`.
|
|
|
|
```js
|
|
assert.strictEqual(infiniteStringTour(), 9922545104535660);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function infiniteStringTour() {
|
|
|
|
return true;
|
|
}
|
|
|
|
infiniteStringTour();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|