55 lines
1.2 KiB
Markdown
55 lines
1.2 KiB
Markdown
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---
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id: 5900f4f81000cf542c51000b
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title: 'Problem 396: Weak Goodstein sequence'
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challengeType: 5
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forumTopicId: 302061
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dashedName: problem-396-weak-goodstein-sequence
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---
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# --description--
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For any positive integer n, the nth weak Goodstein sequence {g1, g2, g3, ...} is defined as:
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g1 = n
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for k > 1, gk is obtained by writing gk-1 in base k, interpreting it as a base k + 1 number, and subtracting 1.
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The sequence terminates when gk becomes 0.
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For example, the 6th weak Goodstein sequence is {6, 11, 17, 25, ...}: g1 = 6. g2 = 11 since 6 = 1102, 1103 = 12, and 12 - 1 = 11. g3 = 17 since 11 = 1023, 1024 = 18, and 18 - 1 = 17. g4 = 25 since 17 = 1014, 1015 = 26, and 26 - 1 = 25.
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and so on.
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It can be shown that every weak Goodstein sequence terminates.
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Let G(n) be the number of nonzero elements in the nth weak Goodstein sequence. It can be verified that G(2) = 3, G(4) = 21 and G(6) = 381. It can also be verified that ΣG(n) = 2517 for 1 ≤ n < 8.
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Find the last 9 digits of ΣG(n) for 1 ≤ n < 16.
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# --hints--
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`euler396()` should return 173214653.
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```js
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assert.strictEqual(euler396(), 173214653);
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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 euler396() {
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return true;
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}
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euler396();
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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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