User:Googleaarex/2-Goodstein Sequences - From 12 to 16

12
X*(X*(X+1)), 2

X*(X*X+2)+2, 3

X*(X*X+2), 5

X*(X*X+1), 11

X*(X*X), 23

X*(X*23+23)+23, 23

X*(X*23), f(23)

0, f^24(23)

14
X*(X*(X+1)+1), 2

X*(X*(X+1)), 5

X*(X*X+5)+5, 6

X*(X*X), f(5)

X*(X*f(5)+f(5))+f(5), f(5)

X*(X*f(5)), f(f(5))

0, f^{f(5)+1}(5)

16
X*(X*(X*X)), 2

X*(X*(X*2)+2)+2, 3

X*(X*(X*2)+2), 5

X*(X*(X*2)), 23

X*(X*(X+23)+23)+23, 24

X*(X*(X+23)), f(23)

X*(X*X), f^{f(23)+1}(23)

X*(X*f^{f(23)+1}(23))+f^{f(23)+1}(23), f^{f(23)+1}(23)+1

0, f^{f^{f(23)+1}(23)+1}(f^{f(23)+1}(23))