User blog comment:Ikosarakt1/My Turing machine programs/@comment-25418284-20130328183208/@comment-5150073-20130328191347

Look at my 11 state one. Unlike your, my TM takes two numbers (string of ones) as inputs and doubles the second, first number of times. If you write 111...111 111...111 (n 1's, you get f_2(n) exactly)

0 1 * r 0 0 _ * r 1 1 _ * r 1 1 1 * l 1a 1a _ * r 2 2 _ _ l 3 2 1 _ r 3 3 1 * r 3 3 _ * r 4 4 _ 1 r 5 4 1 * r 4 5 _ 1 l 6 6 _ * l 7 6 1 * l 6 7 _ * r 8 7 1 * l 7 8 _ * l 9 8 1 _ r 3 9 _ * l 9 9 1 _ l 10 10 _ * l halt 10 1 * r 0