Let $x(n)$ be the power tower $2 \uparrow 3 \uparrow 4 \uparrow \cdots \uparrow n$.
Let $y(n)$ be the power tower $n \uparrow (n-1) \uparrow \cdots \uparrow 3 \uparrow 2$
My questions :
Is there a notation and / or a name for those power towers ?
How can the numbers m1 and m2 with the properties
$$10 \uparrow \uparrow m1 < x(n) < 10 \uparrow \uparrow (m1+1)$$
and
$$10 \uparrow \uparrow m2 < y(n) < 10 \uparrow \uparrow (m2+1)$$
be calculated for a given $n$?