59 lines
1.7 KiB
Markdown
59 lines
1.7 KiB
Markdown
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---
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id: 5900f45b1000cf542c50ff6d
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title: 'Problem 238: Infinite string tour'
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challengeType: 5
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forumTopicId: 301883
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dashedName: problem-238-infinite-string-tour
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---
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# --description--
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Create a sequence of numbers using the "Blum Blum Shub" pseudo-random number generator:
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s0 = 14025256 sn+1 = sn2 mod 20300713
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Concatenate these numbers s0s1s2… to create a string w of infinite length. Then, w = 14025256741014958470038053646…
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For a positive integer k, if no substring of w exists with a sum of digits equal to k, p(k) is defined to be zero. If at least one substring of w exists with a sum of digits equal to k, we define p(k) = z, where z is the starting position of the earliest such substring.
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For instance:
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The substrings 1, 14, 1402, … with respective sums of digits equal to 1, 5, 7, … start at position 1, hence p(1) = p(5) = p(7) = … = 1.
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The substrings 4, 402, 4025, … with respective sums of digits equal to 4, 6, 11, … start at position 2, hence p(4) = p(6) = p(11) = … = 2.
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The substrings 02, 0252, … with respective sums of digits equal to 2, 9, … start at position 3, hence p(2) = p(9) = … = 3.
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Note that substring 025 starting at position 3, has a sum of digits equal to 7, but there was an earlier substring (starting at position 1) with a sum of digits equal to 7, so p(7) = 1, not 3.
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We can verify that, for 0 < k ≤ 103, ∑ p(k) = 4742.
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Find ∑ p(k), for 0 < k ≤ 2·1015.
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# --hints--
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`euler238()` should return 9922545104535660.
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```js
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assert.strictEqual(euler238(), 9922545104535660);
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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 euler238() {
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return true;
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}
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euler238();
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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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