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id	title	challengeType	forumTopicId	dashedName
5900f49d1000cf542c50ffb0	Problem 305: Reflexive Position	5	301959	problem-305-reflexive-position

--description--

Let's call S the (infinite) string that is made by concatenating the consecutive positive integers (starting from 1) written down in base 10.

Thus, S = 1234567891011121314151617181920212223242\ldots

It's easy to see that any number will show up an infinite number of times in S.

Let's call f(n) the starting position of the n^{\text{th}} occurrence of n in S. For example, f(1) = 1, f(5) = 81, f(12) = 271 and f(7780) = 111\\,111\\,365.

Find \sum f(3^k) for 1 ≤ k ≤ 13.

--hints--

reflexivePosition() should return 18174995535140.

assert.strictEqual(reflexivePosition(), 18174995535140);

--seed--

--seed-contents--

function reflexivePosition() {

  return true;
}

reflexivePosition();

--solutions--

// solution required

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