Interesting puzzles - 3

1000 people are standing in a circle. The thought police starts killing them alternately till just one is left. Who will be the remaining one? Solve it for a general N.

Elegant solutions get more marks :) [No induction please :)]

eg. if N = 5, ppl get killed in the following order 2 (skip 3),4 (skip 5),1 (skip 3 since 2 is longer there), 5. The survivor is 3.