---
id: 5900f4811000cf542c50ff94
challengeType: 5
title: 'Problem 277: A Modified Collatz sequence'
---

## 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, '<code>euler277()</code> should return 1125977393124310.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler277() {
  // Good luck!
  return true;
}

euler277();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
