User blog:Hl3 or bust/A Newcomer Tries His Hand At a Thing

Welcome to my first attempt to do anything here other than make like 2 edits to the newest croutonillion page and lurk, i hope you find it lacking so i can get the motivation to do something actually good:

Letter Notation part 1:

A(a) = a+1

A1(a)/A1(a) = A(a)

An(a) indicates an iterated function (i.e. A(A(A(....A(A(a))....))) with a A's)

An(a) = An-1An-1 An-1 .... An-1 a(a .... (a) (a) (a) with a A's

$(a) where $ is the nth letter of the english alphabet = @@ @ .... @ a(a) .... (a) (a) (a) with a @'s, where @ is the n-1th letter of the english alphabet

Analysis:

A(a) = F0(a) is the FGH

Aa(a) = F1(a)

A2(a) = F2(a)

in general, Aa(a) ≈ Fw(a) (where w is an ASCII substitute for omega)

B(a) = AA A .... A a(a) .... (a) (a) (a) with a A's ≈ Fw+1(a)

Ba(a) ≈ Fw+2(a)

B2(a) ≈ Fw+3(a)

Ba(a) ≈ Fw+(n+1)(a)

C(a) BB B .... B a(a) .... (a) (a) (a) ≈ F2w+1(a)

D(a) ≈ F3w+1(a)

$(a) where $ is the nth letter of the english alphabet ≈ F(n-1)w+1(a)

with this, we see that Letter Notation part 1 (LNP1), via the function F(n) = $(n) where $ is the nth letter, has a growth rate of w2, which isn't particulary great (roughly equal to {a,a,a,a} in BEAF), but it's a start

(note: i plan on waiting for feedback (if it even comes) before making part 2, mainly to see what people think)