User blog:SuperJedi224/Part 1

The Function
$$F_{n}(x)=F_{0}(F_{n-1}(x-1))+n;F_{0}(x)=2^{x}+1$$

The Numbers
If my calculations are wrong on any of the larger ones, please let me know.

Nillex
$$F_{1}(0)=2(1+\sqrt{2})$$ (noninteger)

Deuteroex
$$F_{1}(2)=10$$

Triex
$$F_{1}(3)=34$$

Tetraex
$$F_{1}(4)=514$$

Decaex/Superiordeuteroex
$$F_{1}(10)\approx 2.68\times10^{154}$$

Grandeuteroex/Deuterodex
$$F_{10}(2)\approx 10^{10^{10^{10^{10^{6.15\times10^{406}}}}}}$$ (noninteger)

Deuteroduex
$$F_{2}(2)=67$$

Triduex
$$F_{2}(3)=1,027$$

Tetraduex
$$F_{2}(4)=171,709,869,187$$

Decaduex
$$F_{2}(10)\approx 10^{6.97\times10^{76}}$$

Superiordeuteroduex
$$F_{2}(67) \approx 10^{1.15\times10^{19}}$$

Deuterotrix
$$F_{3}(2)\approx 2,857,236,295.8$$ (noninteger)

Tritrix
$$F_{3}(3)\approx 1.48\times10^{20}$$

Tetratrix
$$F_{3}(4)\approx 1.44\times10^{309}$$

Decatrix
$$F_{3}(10)\approx 10^{10^{6.17\times10^{37}}}$$