Natural Properties of the Tetra-Euler Number

[JmsNxn]

The way you can think of this base value, as the next \(\eta\). It's actually pretty ugly for tetration. It will involve repelling branches, which when iterated, produce bounded pentations. So \(\eta^4\) is to \(\uparrow^3\) as, \(\eta\) is to \(\uparrow^2\). This becomes much more complicated though, be cause \(\eta^4\) is defined off of a repelling iteration. It does not exist using solely attracting iterations of tetration.