1.4 KiB
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4811000cf542c50ff94 | Problem 277: A Modified Collatz sequence | 5 | 301927 | problem-277-a-modified-collatz-sequence |
--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"?
--hints--
euler277() should return 1125977393124310.
assert.strictEqual(euler277(), 1125977393124310);
--seed--
--seed-contents--
function euler277() {
return true;
}
euler277();
--solutions--
// solution required