Logic Masters Deutschland e.V.

It is about sequences from 1 to N here. Let me give you some examples, from which you can deduce the rules of these sequences.

Examples
Let’s start with 1 to 4. 1, 2, 3, 4 is valid. We can even reverse it and it will still be valid. Actually, it does not matter with how many numbers we do this, a sequence like 1, 2, …, N-1, N will always be valid, and in reverse it still is.

Let’s switch two numbers around, such that we get 1, 2, 4, 3. This is also still a valid sequence according to the rules, but none of the digits remains valid if we reverse the sequence to 3, 4, 2, 1.

Let me just give you one more example - with 1 to 7 - before we get into the real deal.
5, 3, 2, 7, 1, 6, 4. This is valid. However, if we reverse it, not a single number adheres to the rules anymore.

The puzzle
Now, here is the real puzzle:
?, 4, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, 13, ?, ?

Obviously, this has lots of possible solutions. However, if we add some rules, a unique solution is possible with some hard work!
First of all, let’s say the reversed sequence must be completely invalid (not a single number may apply the sequence rules correctly).
In addition, we’re restricting adjacent digits, such that they cannot be consecutive, and their greatest common denominator must be 1.