User blog comment:Deedlit11/Okay, more Turing machines/@comment-10429372-20130927154129/@comment-10429372-20131007163852

I found \Sigma(23) > f_{\omega+1}(3816)<\math>, using this machine: 0 _ 1 r a 0 1 1 l b a _ _ l 0 a 1 _ l c b _ 1 l 0 b 1 _ l 17 c _ 1 l a c 1 1 r d d _ _ r c d 1 _ r a 17 _ 1 l 18 17 1 _ l 15 18 1 1 l 17 18 _ _ l 16 1 1 1 l 1 1 _ 1 r 2 2 1 1 r 2 2 _ _ r 3 3 _ 1 r 14 3 1 1 r 4 4 1 1 l 5 4 _ _ r 6 5 1 _ l 5 5 _ 1 l 1 6 _ 1 r 14 6 1 1 r 7 7 _ _ r 6 7 1 1 l 8 8 1 _ l 9 9 _ _ l 10 9 1 1 r 11 10 1 1 l 9 10 _ 1 r 1 11 1 _ r 12 11 _ _ l 13 12 _ 1 r 11 12 1 1 l 13 13 1 1 l 13 13 _ 1 l 10 14 _ _ l halt 14 1 _ l 8 15 1 1 l 16 15 _ 1 l 1 16 _ _ l 15 16 1 _ l 15 This machine eliminates state 15.