d269909faa
* fix: clean-up Project Euler 381-400 * fix: missing image extension * fix: missing subscripts Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
63 lines
1.4 KiB
Markdown
63 lines
1.4 KiB
Markdown
---
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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 $n$th weak Goodstein sequence $\\{g1, g2, g3, \ldots\\}$ is defined as:
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- $g_1 = n$
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- for $k > 1$, $g_k$ is obtained by writing $g_{k - 1}$ in base $k$, interpreting it as a base $k + 1$ number, and subtracting 1.
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The sequence terminates when $g_k$ becomes 0.
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For example, the $6$th weak Goodstein sequence is $\\{6, 11, 17, 25, \ldots\\}$:
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- $g_1 = 6$.
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- $g_2 = 11$ since $6 = 110_2$, $110_3 = 12$, and $12 - 1 = 11$.
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- $g_3 = 17$ since $11 = 102_3$, $102_4 = 18$, and $18 - 1 = 17$.
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- $g_4 = 25$ since $17 = 101_4$, $101_5 = 26$, 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 $n$th weak Goodstein sequence.
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It can be verified that $G(2) = 3$, $G(4) = 21$ and $G(6) = 381$.
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It can also be verified that $\sum G(n) = 2517$ for $1 ≤ n < 8$.
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Find the last 9 digits of $\sum G(n)$ for $1 ≤ n < 16$.
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# --hints--
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`weakGoodsteinSequence()` should return `173214653`.
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```js
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assert.strictEqual(weakGoodsteinSequence(), 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 weakGoodsteinSequence() {
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return true;
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}
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weakGoodsteinSequence();
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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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