76 lines
1.6 KiB
Markdown
76 lines
1.6 KiB
Markdown
---
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id: 5900f5411000cf542c510052
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challengeType: 5
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title: 'Problem 467: Superinteger'
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forumTopicId: 302142
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---
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## Description
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<section id='description'>
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An integer s is called a superinteger of another integer n if the digits of n form a subsequence of the digits of s.
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For example, 2718281828 is a superinteger of 18828, while 314159 is not a superinteger of 151.
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Let p(n) be the nth prime number, and let c(n) be the nth composite number. For example, p(1) = 2, p(10) = 29, c(1) = 4 and c(10) = 18.
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{p(i) : i ≥ 1} = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...}
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{c(i) : i ≥ 1} = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, ...}
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Let PD the sequence of the digital roots of {p(i)} (CD is defined similarly for {c(i)}):
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PD = {2, 3, 5, 7, 2, 4, 8, 1, 5, 2, ...}
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CD = {4, 6, 8, 9, 1, 3, 5, 6, 7, 9, ...}
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Let Pn be the integer formed by concatenating the first n elements of PD (Cn is defined similarly for CD).
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P10 = 2357248152
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C10 = 4689135679
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Let f(n) be the smallest positive integer that is a common superinteger of Pn and Cn. For example, f(10) = 2357246891352679, and f(100) mod 1 000 000 007 = 771661825.
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Find f(10 000) mod 1 000 000 007.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler467()</code> should return 775181359.
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testString: assert.strictEqual(euler467(), 775181359);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler467() {
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// Good luck!
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return true;
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}
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euler467();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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