32fac23a2d
* fix: clean-up Project Euler 161-180 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
47 lines
1.1 KiB
Markdown
47 lines
1.1 KiB
Markdown
---
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id: 5900f4141000cf542c50ff26
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title: 'Problem 167: Investigating Ulam sequences'
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challengeType: 5
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forumTopicId: 301801
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dashedName: problem-167-investigating-ulam-sequences
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---
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# --description--
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For two positive integers $a$ and $b$, the Ulam sequence $U(a,b)$ is defined by ${U{(a,b)}\_1} = a$, ${U{(a,b)}\_2} = b$ and for $k > 2$, ${U{(a,b)}\_k}$ is the smallest integer greater than ${U{(a,b)}\_{(k-1)}}$ which can be written in exactly one way as the sum of two distinct previous members of $U(a,b)$.
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For example, the sequence $U(1,2)$ begins with
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$$1, 2, 3 = 1 + 2, 4 = 1 + 3, 6 = 2 + 4, 8 = 2 + 6, 11 = 3 + 8$$
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5 does not belong to it because $5 = 1 + 4 = 2 + 3$ has two representations as the sum of two previous members, likewise $7 = 1 + 6 = 3 + 4$.
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Find $\sum {U(2, 2n + 1)_k}$ for $2 ≤ n ≤ 10$, where $k = {10}^{11}$.
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# --hints--
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`ulamSequences()` should return `3916160068885`.
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```js
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assert.strictEqual(ulamSequences(), 3916160068885);
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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 ulamSequences() {
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return true;
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}
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ulamSequences();
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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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