User blog comment:Deedlit11/Okay, more Turing machines/@comment-10429372-20130927154129/@comment-5529393-20131006230011

Very nice find! It appears that the trick of going to state 8 rather than state 1 will work on the original TM as well, so we can get a 24-state machine that writes more than $$f_{\omega+1}(6143)$$ ones with the following:

So $$ \Sigma(24) > f_{\omega+1}(6143)$$. Awesome!