The requirements state that a permutation of first N positive integers is beautiful if
For every i < j, there is no k with i < k < j such that nums[k] * 2 = nums[i] + nums[j].

It asks for any such array to be returned. But the test case for n=4 has only a single accepted answer. I find 10 different beautiful permutations for n=4. Of course I am returning the first one encountered, since any is expected. The test case only includes one of the possible answers.

The 10 permutations matching the requirements to be beautiful are:
(1, 3, 2, 4)
(1, 3, 4, 2)
(2, 1, 4, 3)
(2, 4, 1, 3)
(2, 4, 3, 1)
(3, 1, 2, 4)
(3, 1, 4, 2)
(3, 4, 1, 2)
(4, 2, 1, 3)
(4, 2, 3, 1)

I return [1,3,2,4], but the test case expects [2,1,4,3] only.