andydude Wrote:http://tetration.itgo.com/newtxt/table-tetbin.txt

Wow, that's an extensive and interesting table. I especially like the values below -2.

Ivars Wrote:If in series there is 1/n!, then formula becomes:

n= ln(2) * ((1-exp(-x))/x)

if just 1/n, then:

n= ln(2) * (ln(1+x)/x)

Nope, neither of them worked. But hey, it was worth trying.

Meanwhile, I figured out linear parameters for 3^^x.

With n = 0.0813-0.328823x, for 0 < x < 1: 3^^x ~~ [x(3^n-1)+1]^(1/n)

Again, quite close, but still with minimal irregularities.

Either I didn't try long enough to find exact parameters, or I'm really on the wrong track. (Most probably the latter. (Then again, thinking about n to be a polynomial of infinite degree or some other equation ... nah, I leave that to someone else who's interested.))