User blog:Nayuta Ito/My Salad Number

Inspired by croutonillion.

First, C(0)=googoltriplex.

Starting for X=C(n) and this is how to get C(n+1):

0. X^^^...^^^X (X copies of ^) 1. repeat step 0 for X![C(0),C(1),...,C(n-2),C(n-1),C(n)] times 2. repeat step 0-1 for X![C(0),C(1),...,C(n-2),C(n),C(n-1)] times 3. repeat step 0-2 for X![C(0),C(1),...,C(n-1),C(n-2),C(n)] times ... n!. repeat step 0-(n!-1) for X![C(n),C(n-1),...,C(2),C(1),C(0)] times 1'. X+C(0) 2'. X+C(1) ... n'. X+C(n) n+1'. X+C(0)+C(1) ... (do all combinations) ... 2^n'. X+C(0)+C(1)+...,C(n-1)+C(n) 2^n+1'. X*C(0) ... (do the same thing as plus) (do the same thing until arrow becomes C(n)) ... 1. X{([tel:[tel:7625597484987 7625597484987] 7625597484987](([tel:[tel:7625597484987 7625597484987] 7625597484987])↑7625597484987([tel:[tel:7625597484986 7625597484986] 7625597484986])↑7625597484987([tel:[tel:7625597484985 7625597484985] 7625597484985])↑7625597484987 ([tel:[tel:7625597484984 7625597484984] 7625597484984])....↑7625597484987(3)↑7625597484987(2))![C(0)]}X 2. X{([tel:[tel:7625597484987 7625597484987] 7625597484987](([tel:[tel:7625597484987 7625597484987] 7625597484987])↑7625597484987([tel:[tel:7625597484986 7625597484986] 7625597484986])↑7625597484987([tel:[tel:7625597484985 7625597484985] 7625597484985])↑7625597484987 ([tel:[tel:7625597484984 7625597484984] 7625597484984])....↑7625597484987(3)↑7625597484987(2))![C(0),C(1)]}X ... n''. X{([tel:[tel:7625597484987 7625597484987] 7625597484987](([tel:[tel:7625597484987 7625597484987] 7625597484987])↑7625597484987([tel:[tel:7625597484986 7625597484986] 7625597484986])↑7625597484987([tel:[tel:7625597484985 7625597484985] 7625597484985])↑7625597484987 ([tel:[tel:7625597484984 7625597484984] 7625597484984])....↑7625597484987(3)↑7625597484987(2))![C(0),C(1),...C(n)]}X

Now, start with C(100).


 * 1) C(X)
 * 2) C(C(X))
 * 3) C(C(C(X)))
 * 4) C(C(...C(C(X))...)) /w X C's
 * {X,X,2} solved like BEAF with {a,b}=C(C(...C(a)...)) /w b C's
 * {X,X,X} solved like BEAF with {a,b}=C(C(...C(a)...)) /w b C's
 * {X,X,1,2} solved like BEAF with {a,b}=C(C(...C(a)...)) /w b C's
 * {X,X,X,2} solved like BEAF with {a,b}=C(C(...C(a)...)) /w b C's
 * {X,X,X,X} solved like BEAF with {a,b}=C(C(...C(a)...)) /w b C's
 * {X,X,X,X,X}
 * {X,X(1)2}
 * {X,X(1)3}
 * {X,X(1)X}
 * {X,X(1)1,2}
 * {X,X(1)X,2}
 * {X,X(1)X,X}
 * {X,X(1)(1)2}
 * {X,X(2)2}
 * {X,X(3)2}
 * {X,X(X)2}
 * {X,X(0,X)2}
 * {X,X((1)1)2}