User blog comment:Nayuta Ito/PEGG detailed log/L/@comment-5.170.74.252-20180810195615/@comment-30754445-20180811175814

lavio,

Nayuta Ito never maintained a table of the kind you're talking about. You're probably confusing this page of his (which logs pas values of PEGG) with the page he linked to (which maintains a detailed table of the sort you're looking for, but only for the lastest value)

Both pages aren't updated every day, by the way.

At any rate, there's a simple way to translate Letter Notation to arrows:

En= 10↑n

Fn = 10↑↑n

Gn = 10↑↑↑n

Hn = 10↑↑↑↑n

Jn = 10 [n arrows] 10

Kn = a Graham-Number style structure with n layers, with a "10" at the top.

The last one may seem a little confusing, so as an example:

K2 = 10 [10 arrows] 10

K3 = 10 [K2 arrows] 10

K4 = 10 [K3 arrows] 10

And so on.

With multiple letters, you simply do the operations one after the other (from right to left) so:

FE3 = 10↑↑10↑3 = 10↑↑1000 = a power tower of 1000 tens.

Also,.the subscript numbers tell you how many times to repeat any operation.

So:

G4FE265 = 10↑↑↑ 10 ↑↑↑ 10↑↑↑ 10↑↑↑ 10↑↑ 10↑ 10↑ 65

(spaces added for clarity)

For a larger example, look my page that Nayuta Ito linked to, which currently holds the PEGG value for August 9. In letter notation, the number is:

K6G6F5E3(7.772x10244)

I strongly recommend that you take the time to examine how the above expression (combined with the "translation guide" I've just given you) results in the arrow structure given above the table. Once you get how it was done this time, you'll be able to figure out the arrow representation for today's number on your own.

For future dates, you should keep another thing in mind:

Sometimes the given arrow and letter representations would seem to be at odds with each other. This is simply because the arrow version was rounded to fit the width of the page.

For similar rounding reasons, the letters given by Nayuta Ito would sometimes differ than the ones given by me. For example, on August 7, the table here gives K6G12 while my table gave it as K6F10E85(2.7x10 28</sup). Both approximations are correct. The only difference is the point each of us chose to stop the calculation

(the actual value of that day's PEGG was K6G12.10987... Nayuta Ito just rounded the last number to 12 and stopped there, while I continued to actually calculate "G12.10987...". His method makes the progression of the numbers clearer, while my method gives more accurate values)