Problem of the Week 982

A Sliding Coin Puzzle

Start with the sequence of coins as follows (where you can think of O as TAILS and X as HEADS; there are 14 tails and 15 heads)

XOXOXOXOXOXOXOXOXOXOXOXOXOXOX

Transform it to

XXXXXXXXXXXXXXXOOOOOOOOOOOOOO

using moves of the following sort:

Take two consecutive coins and move them to the end, or the beginning.

A general algorithm for the n/n+1 problem is welcome, perhaps with bounds on the number of moves.

Source: Suggested by Steven Tedford, Franklin and Marshall College