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

I can prove $$\Sigma(24) > f_{\omega+1}(3817)$$, using this 5 state busy beaver: 0 _ 1 r 1 0 1 1 l 2 1 _ _ l 0 1 1 _ l 5 2 _ 1 l 0 2 1 1 l halt 3 _ 1 l 1 3 1 1 r 4 4 _ _ r 3 4 1 _ r 1 It outputs

$$(1_)^190911_1111$$ where the head is on the _ before the last one

Using 0 _ 1 l 1 1 1 1 l 0 1 _ _ l 8 ;8 means state 8 of Deedlit's expandal growth machine we can change this to $$1^3820_1111$$ before entering state 8.

So it will be $$11__1^3820_1111$$ where the head is on the second 1 when the machine starts in state 0.

I used 7 states to set input, so $$\Sigma(24) > f_{\omega+1}(3817)$$