User blog:O.murphy.b.123/Béktelsson's Exponential Triangle Sequence

Today I created a sequence of numbers called the Bektelsson Exponential Triangle Sequence (or BExTr[]) In this sequence BExTr[a] = the first a triangular numbers ^^^^... ^^^ to each other in which there are a - 3 arrows.

The number 1 is not considered a triangular number in this function, because that would lead to an infinite loop of ones

For example, BExTr[1] = 3

BExTr[2] = 3 + 6 = 9

BExTr[3] = 3 x 6 x 10 = 180

BExTr[4] = 3 ^ 6 ^ 10 ^ 15

BExTr[5] = 3 ^^ 6 ^^ 10 ^^ 15 ^^ 21

BExTr[6] = 3 ^^^ 6 ^^^ 10 ^^^ 15 ^^^ 21 ^^^ 28

And so on.

I have created the suffix -suuri, so that a-suuri = BExTr[a]

Tensuuri = BExTr[10]

Hundredsuuri = BExTr[100]

Thousandsuuri = BExTr[1000]

BExTr[googol] = googolsuuri = schmoogol

Bischmoogol = BExTr[schmoogol]

Trischmoogol = BExTr[bischmoogol]

I will now introduce the schmoogolF[] function. In this function, schmoogolF[a] = BExTr[schmoogolF[a-1]] and schmoogolF[0] = googol.

So schmoogol = schmoogolF[1]

bischmoogol = schmoogolF[2]

trischmoogol = schmoogolF[3]

quaschmoogol = schmoogolF[4]

quischmoogol = schmoogolF[5]

sexteschmoogol = schmoogolF[6]

septeschmoogol = schmoogolF[7]

...

and so on.

-  Ólaf Murphy Béktelsson