User blog comment:PsiCubed2/An intuitive lexicographic ordering of numbers up to P10 (ω^ω-level)/@comment-30004975-20170510034026/@comment-30754445-20170510092523

MM10 = N2.0$3

In general, for a>1, 0≤b<10, 1<c<10 we have:

(a,b+1)|c = Na.b$c

Technically and formally, the decimal point isn't needed. N20$3 is also valid. I would avoid it, though, because "N20..." gives the impression of a number between (20,0)|10 and (21,0)|10.

As for P, it goes like this:

(a,b,c,d,...,k+1)|n = P(number of entries in the array - 1)-abcdk$n

(assuming all numbers are less then 10)

So:

(1,3,5,2,6,4,3,2,8,6)|7 will be written as P9-1352643285$7

If n=10, then we the string after the dash would be "abcd...k" and no $:

(1,3,5,2,6,4,3,2,8,6)|10 will be simply P9-1352643286

Note that if the array ends with one or more zeros, it can be rewritten as one which doesn't end in that way:

(1,3,5,2,6,4,3,2,8,0)|6 = (1,3,5,2,6,4,3,2,7,6)|10 = P9-1352643276

and

(1,3,5,0,0,0,0,0,0,0)|6 = (1,3,4,9,9,9,9,9,9,10)|10 = P9-1349999999