Golden Tommy Numbers

[tommy1729]

Consider the Fibonacci or tribonacci like recursion

F(k) = f(1) + f(2) + ... + f(k-n)

This leads us to the related golden Tommy Numbers

G(n) for n a strict + integer,
The largest real root of :


x^n - x^(n-1) = 1

I know that g(1) till g(5) can be given by radicals and that g(1) = 2, g(2) = the golden mean.
Also lim g(n) = 1.

What else do we know about these numbers ?

Regards

Tommy1729

[tommy1729]

Sorry belongs in community or main.

[tommy1729]

G(n) grows like 1 + exp(2)/n.
I find it fascinating.

Regards

Tommy1729