Maths for nutters. I have a round table with twelve seats. Can I sit in each of the twelve places?

omitting none and repeating none, but moving by a different number of seats each time? eg Seat No. 1, then shift two spaces to seat no. 3, then shift one space to seat no. 4, then shift five spaces to seat no. 9 etc. Moving a different distance each time and covering all the twelve seats with no repeats.Is there a way of working this out?