Problem 42754. Odd elimination

Inspired by Project Euler problem #539

You'll be given a vector from 1 to n;

Going from left to right, remove the first number and every other number afterward until the end of the list.

Repeat the procedure from right to left, removing the right most number and every other number from the numbers left. Continue removing every other numbers, alternating left to right and right to left, until a single number remains.

Example with n=9

1 2 3 4 5 6 7 8 9

2 4 6 8

2 6

6