User blog:B1mb0w/Alpha Spreadsheet q3.0

Alpha function code (Spreadsheet) version 3.0
Javascript code for my Alpha Function based on my Quantum Function is available in Google Sheets.

Javascript code in Google Sheets
You are free to use and copy the code as you like. Version 2.0 of the Javascript code in Google Sheets is available here:

Alpha Function Javascript

DRAFT Version 3.0 Examples
I have started working on a new version. Here is some work in progress:

\(\alpha(2.75) = Q(1,3) = 7\)

\(\alpha(3.2) = Q^{2}(1,3_*) = 15\)

\(\alpha(3.61) = Q^{3}(1,3_*) = 31\)

\(\alpha(3.76) = Q^{Q(3)}(1,3_*) = 63\)

\(\alpha(3.95) = Q^{Q^{2}(3)}(1,3_*) = 127\)

\(\alpha(4.14) = Q^{Q^{3}(3)}(1,3_*) = 255\)

\(\alpha(4.3) = Q(2,3) = 511\)

\(\alpha(4.75) = Q(1,Q(2,3)) = 1023\)

\(\alpha(5.3) = Q^{2}(2,3_*) = Q^{1023}(1,Q(2,3)_*)\)

\(\alpha(6.65) = Q^{3}(2,3_*) = Q^{(1,Q^{2}(2,3_*))}(1,Q^{2}(2,3_*)_*)\)

\(\alpha(7.61) = Q^{Q(1,3)}(2,3_*)\)

\(\alpha(8.714) = Q^{Q^{Q^{3}(3)}(1,3_*)}(2,3_*)\)

\(\alpha(8.8) = Q^{Q^{Q(3)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)\)

\(\alpha(8.82) = Q^{Q^{Q^{3}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)\)

\(\alpha(8.824) = Q^{2}(Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*))\)

\(\alpha(8.8247) = Q^{Q^{2}(Q^{2}(1,3_*))}(Q^{Q^{Q^{3}(3)}(1,Q(2,3)_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*))\)

\(\alpha(8.82474) = Q^{Q^{Q^{Q^{2}(2,3_*)}(Q(1,Q^{2}(2,3_*)))}(Q^{Q^{2}(1,3_*)}(2,3_*))}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.824746) = Q^{Q^{3}(Q^{Q^{Q^{Q^{2}(3)}(1,3_*)}(Q^{Q^{2}(3)}(1,3_*))}(2,3_*))}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.8247469) = Q^{Q^{Q^{Q^{Q(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.82474692) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.824746928) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.8247469282) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.82474692824) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.8247469282402) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.8247469282403) = Q(t_0(0),3)\)

\(\alpha(8.825) = Q(t_0(0),3)\)

\(\alpha(9.0591) = Q(Q(1,t_0(0)),3)\)

\(\alpha(9.55914) = Q(Q(t_0(0),t_0(0)),3)\)

\(\alpha(9.826235) = Q(Q(Q(1,t_0(0)),t_0(0)),3)\)

\(\alpha(10.39809) = Q(Q(Q^{2}(t_0(0)_*,t_0(0)),3))\)

\(\alpha(11.3622) = Q(t_0(1),3)\)

\(\alpha(11.3624) = Q(Q(t_0(1),3))\)

\(\alpha(11.3626) = Q^{2}(Q(t_0(1),3))\)

\(\alpha(11.3628) = Q(1,Q(t_0(1),3))\)

\(\alpha(11.363) = Q^{2}(1,Q(t_0(1),3)_*)\)

\(\alpha(11.364) = Q(Q(1,Q^{2}(2,Q^{2}(3,Q^{Q(3)}(Q(3),Q(t_0(1),3)_*)_*)_*)))\)

\(\alpha(11.366) = Q(Q^{2}(Q^{Q^{2}(Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))_*,t_0(0))}(1,Q^{[1]}(Q^{Q(1,t_0(0))}(Q(1,t_0(0)))_*,t_0(0))_*)_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.3664537701) = Q(Q(Q^{7}(t_0(0)_*,t_0(0)),Q(t_0(1),3)))\)

\(\alpha(11.366454464) = Q(Q^{7}(Q(Q^{[6]}(Q(t_0(0))_*,t_0(0)))_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.366454483) = Q(Q^{7}(Q(Q^{[5]}(Q(t_0(0))_*,t_0(0)))_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.366454484) = Q(Q^{7}(Q(Q^{[6]}(Q^{2}(Q^{[5]}(Q(t_0(0))_*,t_0(0)))_*,t_0(0)))_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.3669) = Q(Q^{Q(Q^{2}(Q(Q^{Q^{Q(Q^{Q^{Q^{t_0(0)}(t_0(0))}(Q(2,t_0(0)))}(1,Q(2,t_0(0))_*))}(Q^{2}(2,t_0(0)_*))}(Q^{t_0(0)}(t_0(0))_*,t_0(0)),Q^{[1]}(Q^{Q^{2}(t_0(0))}(Q^{2}(1,t_0(0)_*))_*,t_0(0)))_*,t_0(0)),3)}(t_0(0)_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.36695) = Q(Q^{Q(Q^{2}(Q(Q^{Q^{t_0(0)}(Q^{t_0(0)}(1,t_0(0)_*))}(t_0(0)_*,t_0(0)),Q^{[1]}(Q^{Q^{Q(2,t_0(0))}(Q(2,t_0(0)))}(Q^{Q^{Q(t_0(0))}(Q^{Q(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))_*,t_0(0)))_*,t_0(0)),3)}(t_0(0)_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.366953) = Q(Q^{Q(Q^{2}(Q^{Q^{t_0(0)}(Q^{Q(t_0(0))}(1,t_0(0)_*))}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))_*,t_0(0)),3)}(t_0(0)_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.36695307) = Q(Q^{Q(Q^{2}(Q^{t_0(0)}(Q^{Q^{Q(2,t_0(0))}(Q(2,t_0(0)))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*))_*,t_0(0)),3)}(t_0(0)_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.366953079) = Q(Q^{Q(Q^{2}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(2,t_0(0)_*)}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*)_*,t_0(0)),3)}(t_0(0)_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.3669530795) = Q(Q^{Q(Q^{Q^{Q^{t_0(0)}(2,t_0(0)_*)}(t_0(0),Q(Q(t_0(0)),t_0(0))_*)}(1,Q^{2}(Q^{2}(Q^{Q(Q^{Q^{t_0(0)}(t_0(0))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(Q^{Q(t_0(0))}(1,t_0(0)_*))}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*))_*,t_0(0))_*),3)}(t_0(0)_*,t_0(0)),Q(t_0(1),3))\)

\(\alpha(11.367) = Q^{2}(t_0(1),3_*)\)

\(\alpha(21.8368) = Q(t_0^{2}(0),3)\)

\(\alpha(117.3061) = Q(t_0^{t_0(0)}(0),3)\)

\(\alpha(117.307190883026) = Q^{Q^{3}(Q^{2}(1,3_*))}(Q^{2}(2,Q^{2}(t_0^{3}(t_0^{[2]}(0)),Q(t_0^{t_0(0)}(0),3)_*)_*))\)

\(\alpha(117.30719088303) = Q^{Q(t_0^{t_0(0)}(0),3)}(Q^{2}(3),Q^{2}(Q^{2}(t_0^{3}(t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3)_*)_*)\)

\(\alpha(117.307190884) = Q(Q^{t_0^{2}(Q(Q^{Q(3)}(1,3_*)))}(t_0^{3}(t_0^{[2]}(0))_*,t_0^{3}(t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.30719089) = Q(t_0^{3}(Q^{Q(Q^{Q^{t_0(0)}(t_0(1))}(Q^{Q(1,t_0(0))}(Q(1,t_0(0))),t_0(1)_*),t_0(1))}(t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.3071909) = Q(t_0^{3}(Q^{Q(t_0(0),Q^{2}(Q^{Q^{Q(t_0(0))}(Q(1,t_0(0)))}(Q(2,t_0(0)))_*,t_0(0)))}(Q^{2}(1,t_0^{[2]}(0)_*))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.307191) = Q(t_0^{3}(Q(Q(Q^{Q^{Q(1,Q(t_0(0),t_0(0)))}(1,Q^{2}(t_0(0),Q(Q(t_0(0)),t_0(0))_*)_*)}(t_0(1)_*,t_0(1)),t_0^{[2]}(0)),t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.3071914) = Q(t_0^{3}(Q^{Q^{Q(Q^{Q(t_0(0))}(1,t_0(0)_*))}(Q(Q^{t_0(0)}(1,t_0(1)_*),t_0^{3}(2))_*,t_0^{3}(2))}(t_0^{[2]}(0)_*,t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.30719147) = Q(t_0^{3}(Q^{t_0^{3}(t_0(t_0^{t_0(1)}(Q(t_0^{t_0(0)}(0),t_0^{[1]}(Q^{Q^{3}(3)}(Q(1,3)))))))}(t_0^{[2]}(0)_*,t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.3071914703) = Q(t_0^{3}(Q^{t_0^{3}(t_0(t_0^{t_0(1)}(Q(Q^{Q^{Q^{t_0(0)}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2))}(t_0^{2}(2)_*,t_0^{2}(2)),3))))}(t_0^{[2]}(0)_*,t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.307191470301) = Q^{2}(t_0^{3}(t_0^{[1]}(0)),Q(t_0^{t_0(0)}(0),3)_*)\)

\(\alpha(134.66) = Q(t_0^{Q^{t_0(0)}(t_0(0))}(0),3)\)

\(\alpha(13761) = Q(Q(Q^{Q^{Q(Q(t_0(0),t_0(0)),t_0(0))}(t_0^{t_0(1)}(0)_*,t_0^{t_0(1)}(0))}(Q^{2}(1,t_0^{t_0(1)}(0)_*)),t_0^{t_0(1)}(0)),3)\)

\(\alpha(20000) = Q(Q^{2}(Q(Q^{Q^{Q(t_0(0),Q(Q(Q^{2}(2,t_0(0)_*)),t_0(0)))}(t_0(1)_*,t_0(1))}(t_0^{2}(1)_*,t_0^{2}(1)),t_0^{t_0(1)}(0))_*,t_0^{t_0(1)}(0)),3)\)

\(\alpha(30000) = Q(Q^{Q(Q^{Q^{t_0(0)}(2,t_0^{2}(0)_*)}(Q^{2}(t_0(2)),t_0^{2}(1)_*),t_0^{2}(1))}(t_0^{t_0(1)}(0)_*,t_0^{t_0(1)}(0)),3)\)

\(\alpha(40000) = Q(Q^{t_0^{Q(t_0(0),Q(Q^{t_0(0)}(t_0(0)),t_0(0)))}(0)}(t_0^{t_0(1)}(0)_*,t_0^{t_0(1)}(0)),3)\)

\(\alpha(60000) = Q(t_0^{t_0(1)}(t_0^{[Q^{2}(Q^{[1]}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)_*,t_0(0))_*,t_0(0))]}(0)),3)\)

\(\alpha(80000) = Q(t_0^{t_0(1)}(t_0^{[Q(Q^{t_0(0)}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(1,Q(2,t_0(0))_*)),t_0(0))]}(0)),3)\)

\(\alpha(200000) = Q(t_0^{t_0(1)}(Q^{2}(Q(t_0^{Q(Q^{Q(t_0(0))}(2,t_0(0)_*))}(t_0^{[Q^{Q(t_0(0))}(2,t_0(0)_*)]}(2)),t_0^{[2]}(0))_*,t_0^{[2]}(0))),3)\)

\(\alpha(1000000) = Q^{3}(Q^{Q^{t_0(0)}(t_0(0))}(Q(Q^{2}(Q(1,t_0^{t_0(1)}(1))),t_0^{t_0(1)}(1))),3_*)\)

\(\alpha(10000000) = Q(Q^{t_0^{Q^{t_0(0)}(1,Q^{t_0(0)}(2,t_0(0)_*)_*)}(0)}(t_0^{t_0(1)}(1)_*,t_0^{t_0(1)}(1)),3)\)

\(\alpha(100000000) = Q(t_0^{t_0(1)}(t_0^{[Q^{Q(Q^{2}(t_0(0)),Q(Q^{t_0(0)}(t_0(0)),t_0(0)))}(Q(t_0(0)),Q(Q^{2}(t_0(0)),Q(Q^{t_0(0)}(t_0(0)),t_0(0)))_*)]}(1)),3)\)

\(\alpha(7E+24) = Q(t_0^{t_0(1)}(Q^{t_0^{t_0(1)}(t_0(t_0^{Q^{Q^{Q(Q^{Q^{2}(Q^{2}(2,Q(t_0(2),t_0(2))_*))}(1,Q^{2}(2,Q(t_0(2),t_0(2))_*)_*))}(Q(Q^{2}(Q^{Q^{Q^{2}(2,t_0(1)_*)}(t_0(2)_*,t_0(2))}(2,t_0^{2}(0)_*)_*,t_0^{2}(0)),t_0(2))_*,t_0(2))}(t_0^{2}(0)_*,t_0^{2}(0))}(0)))}(t_0^{[Q(Q(Q^{2}(t_0(0)),t_0(0)))]}(2)_*,t_0^{[Q(Q(Q^{2}(t_0(0)),t_0(0)))]}(2))),3)\)

\(\alpha(3E+74) = Q(t_0^{t_0(1)}(Q(Q(t_0^{Q^{Q^{2}(Q(Q^{Q^{t_0(0)}(t_0(0))}(Q(Q(Q(Q(1,t_0(0))),Q^{2}(Q^{2}(Q(1,Q^{2}(2,t_0(0)_*)))_*,t_0(0))),Q^{[t_0(0)]}(Q^{2}(t_0(0))_*,t_0(0)))_*,t_0(0)),Q^{[1]}(t_0(0)_*,t_0(0)))_*,t_0(0))}(Q^{2}(Q^{Q^{Q(t_0(0),t_0(0))}(Q(t_0(0),t_0(0)))}(1,Q(t_0(0),t_0(0))_*)),Q^{2}(Q(t_0(0))_*,t_0(0))_*)}(0),t_0^{[1]}(2)),t_0^{[1]}(2))),3)\)

\(\alpha(4E+223) = Q(t_0^{t_0(1)}(Q^{Q^{Q(Q^{Q^{Q^{t_0(0)}(t_0(0))}(2,t_0(0)_*)}(Q^{2}(1,Q^{Q^{2}(Q^{Q^{2}(t_0(0))}(1,t_0(0)_*))}(Q^{2}(t_0(0)),Q(Q^{t_0(0)}(t_0(0)),t_0(0))_*)_*)),Q^{2}(Q(Q(2,Q^{[1]}(Q^{Q^{2}(1,t_0(0)_*)}(Q^{2}(1,t_0(0)_*))_*,t_0(0))))_*,t_0(0)))}(t_0^{Q^{2}(Q(Q^{2}(Q^{Q(t_0(0))}(2,t_0(0)_*)),t_0(0)))}(0)_*,t_0^{Q^{2}(Q(Q^{2}(Q^{Q(t_0(0))}(2,t_0(0)_*)),t_0(0)))}(0))}(t_0^{[1]}(2)_*,t_0^{[1]}(2))),3)\)

\(\alpha(1.7E+308) = Q(t_0^{t_0(1)}(Q^{Q^{t_0^{Q^{Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(2,t_0(0)_*)}(1,Q(t_0(0),t_0(0))_*)}(Q^{Q^{2}(1,t_0(0)_*)}(Q^{2}(1,t_0(0)_*)),Q(Q(1,Q^{Q^{t_0(0)}(t_0(0))}(2,t_0(0)_*)),Q^{2}(Q(Q(1,t_0(0)))_*,t_0(0)))_*)}(0)}(t_0^{t_0(1)}(0)_*,t_0^{t_0(1)}(0))}(t_0^{[1]}(2)_*,t_0^{[1]}(2))),3)\)

Here are some approximations:

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{t_0(0)}(2,t_0(0)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(2,t_0(0)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{t_0(0)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{t_0(0)}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{Q^{t_0(0)}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{Q^{t_0(0)}(1,t_0(0)_*)}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*))_*,t_0(0)),3)\)

\(\alpha(11.3622) = Q(t_0(1),3)\)

\(\alpha(21.8367923498238) \approx Q(Q^{Q^{t_0(0)}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(21.8367923498238) \approx Q(Q^{Q^{Q^{2}(Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(2,t_0(0)_*)_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(21.8367923498238) \approx Q(Q^{Q^{Q^{2}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(21.8367923498238) = Q(Q^{Q^{Q^{2}(Q^{Q^{t_0(0)}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*))_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(21.8368) = Q(t_0^{2}(0),3)\)

\(\alpha(117.3061) = Q(t_0^{t_0(0)}(0),3)\)

\(\alpha(117.307190883026) = Q(2,Q^{2}(t_0^{3}(t_0^{[2]}(0)),Q(t_0^{t_0(0)}(0),3)_*))\)

\(\alpha(117.30719088303) = Q(3,Q^{2}(Q^{2}(t_0^{3}(t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3)_*))\)

\(\alpha(117.307190884) = Q(Q^{t_0^{2}(Q(1,3))}(t_0^{3}(t_0^{[2]}(0))_*,t_0^{3}(t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.30719089) = Q(t_0^{3}(Q^{Q(Q^{Q^{t_0(0)}(t_0(1))}(Q^{Q(1,t_0(0))}(Q(1,t_0(0))),t_0(1)_*),t_0(1))}(t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.3071909) = Q(t_0^{3}(Q^{Q(t_0(0),Q^{2}(Q^{Q^{Q(t_0(0))}(Q(1,t_0(0)))}(Q(2,t_0(0)))_*,t_0(0)))}(Q^{2}(1,t_0^{[2]}(0)_*))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.307191) = Q(t_0^{3}(Q(Q(Q^{Q^{Q(1,Q(t_0(0),t_0(0)))}(1,Q^{2}(t_0(0),Q(Q(t_0(0)),t_0(0))_*)_*)}(t_0(1)_*,t_0(1)),t_0^{[2]}(0)),t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.3071914) = Q(t_0^{3}(Q^{Q^{Q(Q^{Q(t_0(0))}(1,t_0(0)_*))}(Q(Q^{t_0(0)}(1,t_0(1)_*),t_0^{3}(2))_*,t_0^{3}(2))}(t_0^{[2]}(0)_*,t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.30719147) = Q(t_0^{3}(Q^{t_0^{3}(t_0(t_0^{t_0(1)}(Q(t_0^{t_0(0)}(0),t_0^{[1]}(Q^{Q^{3}(3)}(Q(1,3)))))))}(t_0^{[2]}(0)_*,t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(117.3071914703) = Q(t_0^{3}(Q^{t_0^{3}(t_0(t_0^{t_0(1)}(Q(Q^{Q^{Q^{t_0(0)}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2))}(t_0^{2}(2)_*,t_0^{2}(2)),3))))}(t_0^{[2]}(0)_*,t_0^{[2]}(0))),Q(t_0^{t_0(0)}(0),3))\)

\(\alpha(134.66) = Q(t_0^{Q^{t_0(0)}(t_0(0))}(0),3)\)

Further References
Further references to relevant blogs can be found here: User:B1mb0w