49 lines
1.0 KiB
Markdown
49 lines
1.0 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,
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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 ∑U(2,2n+1)k for 2 ≤ n ≤10, where k = 1011.
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# --hints--
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`euler167()` should return 3916160068885.
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```js
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assert.strictEqual(euler167(), 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 euler167() {
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return true;
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}
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euler167();
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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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