freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-467-superinteger.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f5411000cf542c510052	Problem 467: Superinteger	5	302142	problem-467-superinteger

--description--

An integer s is called a superinteger of another integer n if the digits of n form a subsequence of the digits of s.

For example, 2718281828 is a superinteger of 18828, while 314159 is not a superinteger of 151.

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.

$$\begin{align} & \{p(i) : i ≥ 1\} = \{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, \ldots \} \\ & \{c(i) : i ≥ 1\} = \{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, \ldots \} \end{align}$$

Let P^D the sequence of the digital roots of \\{p(i)\\} (C^D is defined similarly for \\{c(i)\\}):

$$\begin{align} & P^D = \{2, 3, 5, 7, 2, 4, 8, 1, 5, 2, \ldots \} \\ & C^D = \{4, 6, 8, 9, 1, 3, 5, 6, 7, 9, \ldots \} \end{align}$$

Let P_n be the integer formed by concatenating the first n elements of P^D (C_n is defined similarly for C^D).

$$\begin{align} & P_{10} = 2\,357\,248\,152 \\ & C_{10} = 4\,689\,135\,679 \end{align}$$

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.

Find f(10\\,000)\bmod 1\\,000\\,000\\,007.

--hints--

superinteger() should return 775181359.

assert.strictEqual(superinteger(), 775181359);

--seed--

--seed-contents--

function superinteger() {

  return true;
}

superinteger();

--solutions--

// solution required