82 lines
1.6 KiB
Markdown
82 lines
1.6 KiB
Markdown
---
|
|
id: 5900f4811000cf542c50ff94
|
|
challengeType: 5
|
|
title: 'Problem 277: A Modified Collatz sequence'
|
|
forumTopicId: 301927
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
A modified Collatz sequence of integers is obtained from a starting value a1 in the following way:
|
|
|
|
an+1 = an/3 if an is divisible by 3. We shall denote this as a large downward step, "D".
|
|
|
|
an+1 = (4an + 2)/3 if an divided by 3 gives a remainder of 1. We shall denote this as an upward step, "U".
|
|
|
|
|
|
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".
|
|
|
|
|
|
|
|
|
|
The sequence terminates when some an = 1.
|
|
|
|
|
|
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".
|
|
|
|
|
|
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.
|
|
|
|
|
|
What is the smallest a1 > 1015 that begins with the sequence "UDDDUdddDDUDDddDdDddDDUDDdUUDd"?
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler277()</code> should return 1125977393124310.
|
|
testString: assert.strictEqual(euler277(), 1125977393124310);
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler277() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler277();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
|
|
</section>
|