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This is really salad. Croutonillion gave me this idea.

This is written as QSF(x). Start with QSF(0)=googoltriplex,

If you have QSF(n-1), QSF(n) is made like this ( "X" refers to the result of the previous operation.):

0. X=QSF(n-1)

1. X+QSF(0)

2. X+QSF(1)

...

n+1. X+QSF(n-1)

n+2. X+(QSF(0)+QSF(1))

...

(all combination of QSF(a)+QSF(b) is added here)

...

around n^2/2. X+(QSF(n-2)+QSF(n-1))

next. X+(QSF(0)+QSF(1)+QSF(2))

...

(all combination of QSF(a)+QSF(b)+QSF(c) is added here)

...

(all combination of QSF(a)+QSF(b)+QSF(c)+QSF(d) is added here)

...

around 2^n. X+(QSF(0)+QSF(1)+...+QSF(n-1))

Next, do 1-around 2^n again with "X*" instead of "X+."

Next, do 1-around 2^n again, changing all plus into times.

Next, do previous two lines again, with "X^" instead of "X*."

Next, do 1-around 2^n again, changing all plus into exponentiation.

Then...

Repeat what you have done X![QSF(0),QSF(1),...QSF(n-2),QSF(n-1)] times.

Repeat what you have done X![QSF(0),QSF(1),...QSF(n-1),QSF(n-2)] times.

Repeat what you have done X![QSF(0),QSF(1),...QSF(n-2),QSF(n-1),QSF(n-3)] times.

...(Do that for every single permutation for QSF(n) in order.)

Now you get QSF(n).


Do you think are we finished? This is the beginning!

I will define a number below, which is getting longer in each edition.

Start with QSF(0).

  1. QSF(X)
  2. QSF(QSF(X))
  3. QSF(QSF(QSF(X)))
  4. Keep going on until the number of QSF becomes QSF(0).
  5. X^^...^^X (X ^'s)
  6. Repeat 1-5 X times
  7. Repeat 1-6 X times
  8. QSF^{QSF(X)}(X)
  9. QSF^{QSF^{QSF(X)}(X)}(X)
  10. Keep going on until the number of QSF becomes QSF(0).
  11. \{X(X)X\}
  12. X^X+X^X^X+...+X^^X


This is the Quite-Salad-Number in the version you're looking at.

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