User blog:Username5243/Strong Array Notation googolisms II

Continuing on from my last post.

Part II: Four-Entry Level

Regiments: 18

Gusold Regiment
Order Type \(\omega\)

Members: 29 (316 - 344)

Now let's move on to the next level. First we'll start with s(a,b,1,2). To solve this, start the process and turn the 1,2 to b,1 while changing both the first entries to the base. So s(a,b,1,2) = s(a,a,b,1) = s(a,a,b) = a^^^...^^^a with b arrows. In particular s(a,1,1,2) = s(a,a,1,1) = a^a.

We can say then:

(316) Gusold = s(10,100,1,2) = s(10,10,100)

(317) Gusolduni = s(10,1,1,2) = 10^10

(318) Gosoldabi s(10,2,1,2) = 10^^10

(319) Gusoldaquint = s(10,5,1,2)

(320) Gusoldadec = s(10,10,1,2)

(321) Gusoldamil = s(10,1000,1,2)

(322) Gusoldamyr = s(10,10000,1,2)

...

(323) Gusoldaplex = s(10,gusold)

(324) Gusoldadex = s(10,gusold,2)

(325) Gusoldathrex = s(10,gusold,3)

(326) Gusoldatetrex = s(10,gusold,4)

(327) Gusoldapentex = s(10,gusold,5)

(328) Gusoldahex = s(10,gusold,6)

(329) Gusoldaheptex = s(10,gusold,7)

(330) Gusoldoctex = s(10gusold,8)

(331) Gusoldennex = s(10,gusold,9)

(332) Gusoldadecex = s(10,gusold,10)

...

(333) Goosolsuplex = s(10,s(10,100),1,2)

(334) Gransolsuplex = s(10,s(10,100,2),1,2)

(335) Greasolsuplex = s(10,s(10,100,3),1,2)

(336) Gigansolsuplex = s(10,s(10,100,4),1,2)

(337) Gorgesolsuplex = s(10,s(10,100,5),1,2)

(338) Gulsolsuplex = s(10,s(10,100,6),1,2)

(339) Gaspsolsuplex = s(10,s(10,100,7),1,2)

(340) Ginorsolsuplex = s(10,s(10,100,8),1,2)

(341) Gargansolsuplex = s(10,s(10,100,9),1,2)

(342) Googonsolsuplex = s(10,s(10,100,10),1,2)

...

(343) Gusoldasuplex = s(10,s(10,100,1,2),1,2)

(344) Gusoldadusuplex = s(10,gusoldasuplex,1,2)

...

Gransold Regiment
Order Type \(\omega+1\)

Members: ?? (345 - 3??)