53 lines
1.4 KiB
Markdown
53 lines
1.4 KiB
Markdown
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---
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id: 5900f4811000cf542c50ff94
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title: 'Problem 277: A Modified Collatz sequence'
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challengeType: 5
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forumTopicId: 301927
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dashedName: problem-277-a-modified-collatz-sequence
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---
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# --description--
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A modified Collatz sequence of integers is obtained from a starting value a1 in the following way:
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an+1 = an/3 if an is divisible by 3. We shall denote this as a large downward step, "D".
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an+1 = (4an + 2)/3 if an divided by 3 gives a remainder of 1. We shall denote this as an upward step, "U".
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an+1 = (2an - 1)/3 if an divided by 3 gives a remainder of 2. We shall denote this as a small downward step, "d".
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The sequence terminates when some an = 1.
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Given any integer, we can list out the sequence of steps. For instance if a1=231, then the sequence {an}={231,77,51,17,11,7,10,14,9,3,1} corresponds to the steps "DdDddUUdDD".
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Of course, there are other sequences that begin with that same sequence "DdDddUUdDD....". For instance, if a1=1004064, then the sequence is DdDddUUdDDDdUDUUUdDdUUDDDUdDD. In fact, 1004064 is the smallest possible a1 > 106 that begins with the sequence DdDddUUdDD.
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What is the smallest a1 > 1015 that begins with the sequence "UDDDUdddDDUDDddDdDddDDUDDdUUDd"?
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# --hints--
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`euler277()` should return 1125977393124310.
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```js
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assert.strictEqual(euler277(), 1125977393124310);
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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 euler277() {
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return true;
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}
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euler277();
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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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