62 lines
1.8 KiB
Markdown
62 lines
1.8 KiB
Markdown
---
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id: 5900f45b1000cf542c50ff6d
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title: 'Problem 238: Infinite string tour'
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challengeType: 5
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forumTopicId: 301883
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dashedName: problem-238-infinite-string-tour
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---
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# --description--
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Create a sequence of numbers using the "Blum Blum Shub" pseudo-random number generator:
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$$
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s_0 = 14025256 \\\\
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s_{n + 1} = {s_n}^2 \\; mod \\; 20\\,300\\,713
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$$
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Concatenate these numbers $s_0s_1s_2\ldots$ to create a string $w$ of infinite length. Then, $w = 14025256741014958470038053646\ldots$
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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.
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For instance:
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The substrings 1, 14, 1402, … with respective sums of digits equal to 1, 5, 7, … start at position 1, hence $p(1) = p(5) = p(7) = \ldots = 1$.
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The substrings 4, 402, 4025, … with respective sums of digits equal to 4, 6, 11, … start at position 2, hence $p(4) = p(6) = p(11) = \ldots = 2$.
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The substrings 02, 0252, … with respective sums of digits equal to 2, 9, … start at position 3, hence $p(2) = p(9) = \ldots = 3$.
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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.
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We can verify that, for $0 < k ≤ {10}^3$, $\sum p(k) = 4742$.
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Find $\sum p(k)$, for $0 < k ≤ 2 \times {10}^{15}$.
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# --hints--
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`infiniteStringTour()` should return `9922545104535660`.
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```js
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assert.strictEqual(infiniteStringTour(), 9922545104535660);
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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 infiniteStringTour() {
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return true;
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}
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infiniteStringTour();
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```
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# --solutions--
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```js
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// solution required
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```
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