397a9f0c3e
* fix: clean-up Project Euler 462-480 * fix: missing image extension * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
66 lines
1.7 KiB
Markdown
66 lines
1.7 KiB
Markdown
---
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id: 5900f5411000cf542c510052
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title: 'Problem 467: Superinteger'
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challengeType: 5
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forumTopicId: 302142
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dashedName: problem-467-superinteger
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---
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# --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 $n$th prime number, and let $c(n)$ be the $n$th composite number. For example, $p(1) = 2$, $p(10) = 29$, $c(1) = 4$ and $c(10) = 18$.
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$$\begin{align}
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& \\{p(i) : i ≥ 1\\} = \\{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, \ldots \\} \\\\
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& \\{c(i) : i ≥ 1\\} = \\{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, \ldots \\}
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\end{align}$$
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Let $P^D$ the sequence of the digital roots of $\\{p(i)\\}$ ($C^D$ is defined similarly for $\\{c(i)\\}$):
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$$\begin{align}
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& P^D = \\{2, 3, 5, 7, 2, 4, 8, 1, 5, 2, \ldots \\} \\\\
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& C^D = \\{4, 6, 8, 9, 1, 3, 5, 6, 7, 9, \ldots \\}
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\end{align}$$
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Let $P_n$ be the integer formed by concatenating the first $n$ elements of $P^D$ ($C_n$ is defined similarly for $C^D$).
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$$\begin{align}
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& P_{10} = 2\\,357\\,248\\,152 \\\\
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& C_{10} = 4\\,689\\,135\\,679
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\end{align}$$
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Let $f(n)$ be the smallest positive integer that is a common superinteger of $P_n$ and $C_n$. For example, $f(10) = 2\\,357\\,246\\,891\\,352\\,679$, and $f(100)\bmod 1\\,000\\,000\\,007 = 771\\,661\\,825$.
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Find $f(10\\,000)\bmod 1\\,000\\,000\\,007$.
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# --hints--
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`superinteger()` should return `775181359`.
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```js
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assert.strictEqual(superinteger(), 775181359);
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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 superinteger() {
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return true;
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}
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superinteger();
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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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