Vases In A Line

Blogging is for chumps, I'm on extended vacation (also known as semi-unemployed). Anyway, time for a puzzle that I found on the forums at xkcd:

There is a museum with N vases they wish to arrange on a display. The vases are such that the first one has a height of 1cm, the second one has height of 2cm, and so on such that the N^th one has a height of N centimeters. The people at the museum wish to arrange the vases in a linear display in a special way, such that if we have three vases with heights a,b,c, with b being the average of a and c, b does not appear between a and c.

The puzzle is to come up with an algorithm that will generate an arrangement of numbers 1 through N such that no number appears between two numbers it is the average of.

So, for example if N=5, we could not have 3 appear anywhere between 2 and 4, or anywhere between 1 and 5, 2 could not appear between 1 and 3, and 4 could not appear between 3 and 5. An acceptable answer there would be (1 5 3 2 4).