We have the sequence of "Eulers" {2.718281828,3.0885322718...} and the sequence of "Etas" {1.44466786,1.6353244967...}.

"Eulers" and "Etas" can be defined as the x-coordinate and y-coordinate of the maximum of the nth order self root.

Conjecture:

The limit of the sequence of "Eulers" is 4.

The limit of the sequence of "Etas" is 2.

Some discussion can be found here

If you can find a better name for these sequences feel free to use it.

"Eulers" and "Etas" can be defined as the x-coordinate and y-coordinate of the maximum of the nth order self root.

Conjecture:

The limit of the sequence of "Eulers" is 4.

The limit of the sequence of "Etas" is 2.

Some discussion can be found here

If you can find a better name for these sequences feel free to use it.