51 lines
1.4 KiB
Markdown
51 lines
1.4 KiB
Markdown
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---
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id: 5900f4a81000cf542c50ffbb
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title: 'Problem 316: Numbers in decimal expansions'
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challengeType: 5
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forumTopicId: 301972
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dashedName: problem-316-numbers-in-decimal-expansions
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---
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# --description--
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Let p = p1 p2 p3 ... be an infinite sequence of random digits, selected from {0,1,2,3,4,5,6,7,8,9} with equal probability.
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It can be seen that p corresponds to the real number 0.p1 p2 p3 ....
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It can also be seen that choosing a random real number from the interval \[0,1) is equivalent to choosing an infinite sequence of random digits selected from {0,1,2,3,4,5,6,7,8,9} with equal probability.
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For any positive integer n with d decimal digits, let k be the smallest index such that pk, pk+1, ...pk+d-1 are the decimal digits of n, in the same order. Also, let g(n) be the expected value of k; it can be proven that g(n) is always finite and, interestingly, always an integer number.
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For example, if n = 535, then for p = 31415926535897...., we get k = 9 for p = 355287143650049560000490848764084685354..., we get k = 36 etc and we find that g(535) = 1008.
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Given that , find
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Note: represents the floor function.
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# --hints--
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`euler316()` should return 542934735751917760.
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```js
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assert.strictEqual(euler316(), 542934735751917760);
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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 euler316() {
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return true;
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}
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euler316();
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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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