1.6 KiB
id, title, challengeType, forumTopicId, dashedName
| 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 a_1 in the following way:
a_{n + 1} = \frac{a_n}{3} if a_n is divisible by 3. We shall denote this as a large downward step, "D".
a_{n + 1} = \frac{4a_n + 2}{3} if a_n divided by 3 gives a remainder of 1. We shall denote this as an upward step, "U".
a_{n + 1} = \frac{2a_n - 1}{3} if a_n divided by 3 gives a remainder of 2. We shall denote this as a small downward step, "d".
The sequence terminates when some a_n = 1.
Given any integer, we can list out the sequence of steps. For instance if a_1 = 231, then the sequence \\{a_n\\} = \\{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 a_1 = 1004064, then the sequence is DdDddUUdDDDdUDUUUdDdUUDDDUdDD.
In fact, 1004064 is the smallest possible a_1 > {10}^6 that begins with the sequence DdDddUUdDD.
What is the smallest a_1 > {10}^{15} that begins with the sequence "UDDDUdddDDUDDddDdDddDDUDDdUUDd"?
--hints--
modifiedCollatzSequence() should return 1125977393124310.
assert.strictEqual(modifiedCollatzSequence(), 1125977393124310);
--seed--
--seed-contents--
function modifiedCollatzSequence() {
return true;
}
modifiedCollatzSequence();
--solutions--
// solution required