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:

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

\(\alpha(3.125) = Q^{2}(1,3_*) = 15\)

\(\alpha(3.625) = Q^{3}(1,3_*) = 31\)

\(\alpha(3.78125) = Q^{Q(3)}(1,3_*) = 63\)

\(\alpha(3.921875) = Q^{Q^{2}(3)}(1,3_*) = 127\)

\(\alpha(4.1125) = Q^{Q^{3}(3)}(1,3_*) = 255\)

\(\alpha(4.3125) = Q(2,3) = 511\)

\(\alpha(6.65) = Q^{3}(2,3_*) = Q^{2}(2,511_*)\)

\(\alpha(8.7125) = Q^{Q^{Q^{3}(3)}(1,3_*)}(2,3_*)\)

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

\(\alpha(8.829) = Q^{2}(t_0(0),3_*)\)

\(\alpha(8.82583) = Q(1,Q(t_0(0),3))\)

\(\alpha(8.827) = Q^{2}(Q(2,Q(t_0(0),3)))\)

\(\alpha(8.83755) = Q(Q(t_0(0)),3)\)

\(\alpha(8.90173) = Q(Q(1,t_0(0)),3)\)

\(\alpha(8.940627) = Q(Q^{t_0(0)}(1,t_0(0)_*),3)\)

\(\alpha(8.953654) = Q(Q^{Q^{2}(t_0(0))}(1,t_0(0)_*),3)\)

\(\alpha(9.0192664) = Q(Q^{t_0(0)}(2,t_0(0)_*),3)\)

\(\alpha(9.059012) = Q(Q(t_0(0),t_0(0)),3)\)

\(\alpha(9.065) = Q^{Q(Q(1,t_0(0)),3)}(1,Q^{2}(Q^{2}(Q^{2}(1,Q(t_0(0),t_0(0))_*)),3_*)_*)\)

\(\alpha(9.1) = Q^{Q(t_0(0),3)}(Q(Q^{t_0(0)}(t_0(0)),t_0(0)),3_*)\)

\(\alpha(9.2) = Q(Q(Q^{Q^{t_0(0)}(1,t_0(0)_*)}(Q^{Q^{2}(t_0(0))}(1,t_0(0)_*)),t_0(0)),3)\)

\(\alpha(9.3) = Q(Q(Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(2,t_0(0)_*),t_0(0)),3)\)

\(\alpha(9.31) = Q(Q^{Q(t_0(0),Q(Q(t_0(0)),t_0(0)))}(Q(t_0(0),t_0(0)),Q^{2}(t_0(0)_*,t_0(0))_*),3)\)

\(\alpha(9.3101) = Q(Q^{Q(Q^{2}(Q^{2}(1,t_0(0)_*)),t_0(0))}(Q(t_0(0),t_0(0)),Q^{2}(t_0(0)_*,t_0(0))_*),3)\)

\(\alpha(9.3102) = Q(Q^{Q(Q(1,Q^{2}(2,t_0(0)_*)),t_0(0))}(Q(t_0(0),t_0(0)),Q^{2}(t_0(0)_*,t_0(0))_*),3)\)

\(\alpha(9.3103) = Q(Q^{Q^{t_0(0)}(Q^{2}(t_0(0)_*,t_0(0)))}(Q(t_0(0),t_0(0)),Q^{2}(t_0(0)_*,t_0(0))_*),3)\)

\(\alpha(9.3104) = Q(Q^{Q^{t_0(0)}(2,Q^{2}(t_0(0)_*,t_0(0))_*)}(Q(t_0(0),t_0(0)),Q^{2}(t_0(0)_*,t_0(0))_*),3)\)

\(\alpha(9.3105) = Q(Q^{Q(t_0(0),Q^{2}(t_0(0)_*,t_0(0)))}(Q(t_0(0),t_0(0)),Q^{2}(t_0(0)_*,t_0(0))_*),3)\)

\(\alpha(9.3105471811) = Q(Q^{Q(Q^{Q^{t_0(0)}(1,t_0(0)_*)}(2,t_0(0)_*),Q^{2}(t_0(0)_*,t_0(0)))}(Q(t_0(0),t_0(0)),Q^{2}(t_0(0)_*,t_0(0))_*),3)\)

\(\alpha(9.3105471812) = Q(Q^{2}(Q(Q^{[1]}(t_0(0),t_0(0)))_*,t_0(0)),3)\)

\(\alpha(9.3105472) = Q(Q^{2}(Q(Q^{[1]}(t_0(0),t_0(0)))_*,t_0(0)),3)\)

\(\alpha(9.311) = Q(Q^{t_0(0)}(Q^{t_0(0)}(t_0(0)),Q^{2}(Q(Q^{[1]}(t_0(0),t_0(0)))_*,t_0(0))_*),3)\)

\(\alpha(9.31112650216) = Q(Q^{Q(Q(t_0(0),t_0(0)),Q^{2}(Q(Q^{[1]}(t_0(0),t_0(0)))_*,t_0(0)))}(Q(Q(t_0(0),t_0(0))),Q^{2}(Q(Q^{[1]}(t_0(0),t_0(0)))_*,t_0(0))_*),3)\)

\(\alpha(9.31112650217) = Q(Q^{2}(Q^{2}(Q^{[1]}(t_0(0),t_0(0)))_*,t_0(0)),3)\)

\(\alpha(9.31112651) = Q(Q^{2}(Q^{2}(Q^{[1]}(t_0(0),t_0(0)))_*,t_0(0)),3)\)

\(\alpha(9.31750290724) = Q(Q^{2}(Q^{Q^{t_0(0)}(Q^{Q^{Q(t_0(0),t_0(0))}(Q(t_0(0),t_0(0)))}(1,Q(t_0(0),t_0(0))_*))}(2,Q^{[1]}(t_0(0),t_0(0))_*)_*,t_0(0)),3)\)

\(\alpha(9.31750290725) = Q(Q^{2}(Q(t_0(0))_*,t_0(0)),3)\)

\(\alpha(9.317503) = Q(Q^{2}(Q(t_0(0))_*,t_0(0)),3)\)

\(\alpha(9.32) = Q(Q^{Q(Q(t_0(0),t_0(0)),Q^{2}(t_0(0)_*,t_0(0)))}(Q(1,Q(2,Q^{2}(Q(t_0(0))_*,t_0(0))))),3)\)

\(\alpha(9.35) = Q(Q(Q(2,t_0(0)),3),Q^{2}(Q(Q^{2}(1,Q^{2}(Q^{t_0(0)}(t_0(0))_*,t_0(0))_*)),3_*))\)

\(\alpha(9.4) = Q(Q^{Q(Q^{t_0(0)}(1,t_0(0)_*),t_0(0))}(1,Q^{2}(Q^{Q^{2}(t_0(0))}(Q(1,t_0(0)))_*,t_0(0))_*),3)\)

\(\alpha(9.5) = Q(Q(Q(Q^{t_0(0)}(1,t_0(0)_*),t_0(0)),Q^{2}(Q^{Q(t_0(0))}(Q^{2}(2,t_0(0)_*))_*,t_0(0))),3)\)

\(\alpha(9.55912205) = Q(Q^{2}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*,t_0(0)),3)\)

\(\alpha(9.55912206) = Q(t_0(1),3)\)

\(\alpha(9.55913) = Q(t_0(1),3)\)

\(\alpha(9.56275) = Q^{Q(Q^{2}(Q^{Q^{t_0(0)}(1,t_0(0)_*)}(2,t_0(0)_*)_*,t_0(0)),3)}(t_0(1),3_*)\)

\(\alpha(9.5627509908) = Q^{Q(Q^{2}(Q^{Q^{t_0(0)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*,t_0(0)),3)}(t_0(1),3_*)\)

\(\alpha(9.5627509909) = Q(Q(t_0(1)),3)\)

\(\alpha(9.56276) = Q(Q(t_0(1)),3)\)

\(\alpha(10.39812) = Q(t_0(2),3)\)

\(\alpha(10.5) = Q(Q(Q^{2}(Q(t_0(0),Q^{[1]}(Q(t_0(0)),t_0(0)))_*,t_0(0)),t_0(2)),3)\)

\(\alpha(11) = Q(Q^{Q^{t_0(0)}(Q(Q^{Q^{2}(t_0(0))}(Q(2,t_0(0))),t_0(0)))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(11.3) = Q(Q^{Q^{Q(Q^{Q(t_0(0))}(1,t_0(0)_*),t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(11.36216115) = Q(Q^{Q^{Q^{2}(Q^{Q^{t_0(0)}(1,t_0(0)_*)}(2,t_0(0)_*)_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(11.36216116) = Q(t_0^{2}(0),3)\)

\(\alpha(11.36217) = Q(t_0^{2}(0),3)\)

\(\alpha(11.5) = Q(Q(Q(Q(Q^{Q^{2}(1,t_0(0)_*)}(Q^{2}(1,t_0(0)_*)),t_0(0)),t_0^{2}(0)),t_0^{2}(0)),3)\)

\(\alpha(12) = Q(t_0^{2}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0^{[1]}(0)_*)),3)\)

\(\alpha(12.4770696) = Q(t_0^{2}(Q^{2}(Q^{Q(Q^{Q^{t_0(0)}(1,t_0(0)_*)}(2,t_0(0)_*),t_0(0))}(2,t_0^{[1]}(0)_*)_*,t_0^{[1]}(0))),3)\)

\(\alpha(12.4770697) = Q(t_0^{2}(1),3)\)

\(\alpha(12.47707) = Q(t_0^{2}(1),3)\)

\(\alpha(13) = Q(Q^{Q^{Q^{2}(Q(Q^{2}(Q(1,t_0(0))_*,t_0(0)),t_0(1))_*,t_0(1))}(t_0^{2}(0)_*,t_0^{2}(0))}(t_0^{2}(1)_*,t_0^{2}(1)),3)\)

\(\alpha(14) = Q(Q(Q(Q^{2}(Q^{t_0(0)}(1,Q^{[1]}(Q^{2}(Q^{2}(1,t_0^{2}(1)_*)),t_0^{2}(1))_*)_*,t_0^{2}(1)),t_0^{2}(2)),t_0^{2}(2)),3)\)

\(\alpha(15) = Q(t_0^{2}(Q(Q^{t_0(0)}(Q^{Q^{2}(1,Q^{2}(2,t_0(0)_*)_*)}(2,t_0^{[1]}(2)_*)),t_0^{[1]}(2))),3)\)

\(\alpha(15.29819587) = Q(t_0^{2}(Q^{2}(Q^{Q(Q^{Q^{t_0(0)}(1,t_0(0)_*)}(2,t_0(0)_*),t_0(0))}(2,t_0^{[1]}(2)_*)_*,t_0^{[1]}(2))),3)\)

\(\alpha(15.29819588) = Q(t_0^{t_0(0)}(0),3)\)

\(\alpha(15.298196) = Q(t_0^{t_0(0)}(0),3)\)

\(\alpha(16) = Q(t_0^{Q^{Q(1,t_0(0))}(Q(1,t_0(0)))}(2),3)\)

\(\alpha(17) = Q(t_0^{Q^{Q^{t_0(0)}(Q^{2}(1,t_0(0)_*))}(2,t_0(0)_*)}(0),3)\)

\(\alpha(18) = Q(t_0^{Q(Q(Q(1,t_0(0))),Q(Q(Q^{2}(1,t_0(0)_*)),t_0(0)))}(0),3)\)

\(\alpha(19) = Q(t_0^{Q(Q^{Q^{t_0(0)}(t_0(0))}(2,t_0(0)_*),t_0(0))}(0),3)\)

\(\alpha(20) = Q(t_0^{Q^{2}(Q(t_0(0),Q^{[1]}(Q^{t_0(0)}(t_0(0)),t_0(0)))_*,t_0(0))}(0),3)\)

\(\alpha(21) = Q(t_0^{Q^{2}(Q^{Q^{t_0(0)}(Q^{2}(1,t_0(0)_*))}(Q(2,t_0(0)))_*,t_0(0))}(0),3)\)

\(\alpha(21.8367923) = Q(t_0^{Q^{2}(Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(2,t_0(0)_*)_*,t_0(0))}(0),3)\)

\(\alpha(21.8367924) = Q(t_0^{t_0(1)}(0),3)\)

\(\alpha(21.8368) = Q(t_0^{t_0(1)}(0),3)\)

\(\alpha(22) = Q(Q(Q^{Q^{t_0(0)}(t_0^{2}(1)_*,t_0^{2}(1))}(1,Q(2,t_0^{t_0(1)}(0))_*),t_0^{t_0(1)}(0)),3)\)

\(\alpha(25) = Q^{Q(1,Q^{Q^{2}(3)}(2,3_*))}(Q^{2}(t_0^{t_0(1)}(2)),3_*)\)

\(\alpha(30) = Q(t_0^{Q(t_0(1))}(Q^{t_0(0)}(t_0^{[t_0(1)]}(0_*))),3)\)

\(\alpha(31) = Q(t_0^{Q(t_0(1))}(t_0^{[Q^{2}(Q^{[1]}(Q^{Q^{t_0(0)}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)),t_0(0))_*,t_0(0))]}(0_*)),3)\)

\(\alpha(32) = Q(t_0^{Q(t_0(1))}(Q^{Q^{t_0(0)}(t_0^{2}(0)_*,t_0^{2}(0))}(Q^{2}(1,t_0^{[2]}(0_*)_*))),3)\)

\(\alpha(33) = Q(t_0^{Q(t_0(1))}(Q^{Q^{t_0(0)}(t_0(0))}(2,t_0^{[1]}(0)_*)),3)\)

\(\alpha(33.716144531) = Q(t_0^{Q(t_0(1))}(Q^{2}(Q^{Q(Q^{Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*),t_0(0))}(2,t_0^{[1]}(0)_*)_*,t_0^{[1]}(0))),3)\)

\(\alpha(33.716144532) = Q(t_0(t_0(1,0)),3)\)

\(\alpha(33.716145) = Q(t_0(t_0(1,0)),3)\)

\(\alpha(33.801066) = Q(t_0(t_0(1,0)),Q(t_0^{t_0(0)}(t_0(1,0)),3))\)

\(\alpha(33.822346) = Q(Q(1,Q(2,t_0^{t_0^{2}(0)}(t_0(1,0)))),3)\)

\(\alpha(33.84364383) = Q(t_0^{t_0^{t_0(0)}(0)}(t_0(1,0)),3)\)

\(\alpha(33.85074779) = Q(t_0^{t_0^{Q(t_0(0),t_0(0))}(0)}(t_0(1,0)),3)\)

\(\alpha(33.85785393) = Q(t_0^{t_0^{Q^{2}(t_0(0)_*,t_0(0))}(0)}(t_0(1,0)),3)\)

\(\alpha(33.8649624) = Q(t_0^{t_0^{t_0(1)}(0)}(t_0(1,0)),3)\)

\(\alpha(33.88) = Q(t_0^{Q^{t_0^{t_0(0)}(0)}(t_0^{Q(t_0(1))}(0)_*,t_0^{Q(t_0(1))}(0))}(t_0(1,0)),3)\)

\(\alpha(33.886302) = Q(t_0(t_0(1,1)),3)\)

\(\alpha(33.886696) = Q(Q^{2}(t_0(t_0(1,1))),3)\)

\(\alpha(33.971849495) = Q(t_0^{t_0(0)}(t_0(1,1)),3)\)

\(\alpha(33.993287) = Q(t_0^{Q^{t_0(0)}(t_0^{t_0(0)}(0))}(t_0(1,1)),3)\)

\(\alpha(34.03622) = Q(t_0^{t_0^{t_0(0)}(t_0(1,0))}(t_0(1,1)),3)\)

\(\alpha(34.0577149) = Q(t_0(t_0(1,2)),3)\)

\(\alpha(34.2303999398) = Q(t_0(t_0(1,t_0(0))),3)\)

\(\alpha(34.273771155) = Q(Q(t_0(t_0(1,t_0(1))),3))\)

\(\alpha(34.7562) = Q(t_0(t_0^{2}(1,0_*)),3)\)

\(\alpha(34.844978318) = Q(t_0(t_0^{2}(1,t_0(t_0^{[1]}(1,0))_*)),3)\)

\(\alpha(34.845081262) = Q(t_0(t_0^{2}(1,Q(t_0(t_0^{[1]}(1,0)))_*)),3)\)

\(\alpha(34.845596) = Q(t_0(t_0^{2}(1,Q(1,t_0(t_0^{[1]}(1,0)))_*)),3)\)

\(\alpha(34.867224726) = Q(t_0(t_0^{2}(1,t_0^{2}(t_0^{[1]}(1,0))_*)),3)\)

\(\alpha(34.89) = Q(t_0(t_0^{2}(1,t_0^{t_0(0)}(t_0^{[1]}(1,0))_*)),3)\)

\(\alpha(35) = Q(t_0^{t_0^{t_0(0)}(0)}(t_0^{2}(1,1_*)),3)\)

\(\alpha(40) = Q(t_0(t_0^{2}(2,Q^{t_0(0)}(t_0^{2}(t_0^{[1]}(2,2))_*,t_0^{2}(t_0^{[1]}(2,2)))_*)),3)\)

\(\alpha(50) = Q(t_0(t_0(t_0^{2}(Q^{2}(Q(2,t_0^{[1]}(2))_*,t_0^{[1]}(2))),0)),3)\)

\(\alpha(60) = Q(t_0^{Q^{t_0(0)}(t_0(1)_*,t_0(1))}(t_0^{2}(1_*)),3)\)

\(\alpha(70) = Q(Q(Q(t_0(t_0(1,0)),t_0(t_0^{2}(2_*))),t_0(t_0^{2}(2_*))),3)\)

\(\alpha(80) = Q(t_0(t_0^{2}(2_*)),3)\)

\(\alpha(90) = Q(t_0(t_0^{2}(t_0^{2}(Q(Q^{t_0(0)}(t_0^{[1]}(0)),t_0^{[1]}(0)))_*)),3)\)

\(\alpha(100) = Q(t_0(t_0^{2}(t_0^{Q(t_0(0),t_0(0))}(0)_*)),3)\)

\(\alpha(110) = Q(t_0(t_0^{2}(t_0^{t_0(1)}(0)_*)),3)\)

\(\alpha(117.30606) = Q(t_0(t_0^{2}(t_0^{Q(t_0(1))}(Q^{2}(Q^{t_0(0)}(2,t_0^{[1]}(0)_*)_*,t_0^{[1]}(0)))_*)),3)\)

\(\alpha(117.30607) = Q^{3}(2,Q(Q(t_0(t_0^{t_0(0)}(1_*))),3)_*)\)

\(\alpha(120) = Q(t_0(t_0^{Q^{t_0(0)}(1,t_0(0)_*)}(1_*)),3)\)

\(\alpha(140) = Q(t_0(t_0^{Q(Q(t_0(0),t_0(1)),t_0(1))}(1_*)),3)\)

\(\alpha(160) = Q(t_0(t_0^{Q(Q^{t_0(0)}(t_0(2)),t_0(2))}(1_*)),3)\)

\(\alpha(180) = Q(t_0(t_0^{Q^{t_0(0)}(t_0(2)_*,t_0(2))}(1_*)),3)\)

\(\alpha(200) = Q(t_0(t_0^{t_0^{2}(t_0^{[1]}(0))}(1_*)),3)\)

\(\alpha(300) = Q(t_0(t_0^{t_0^{2}(Q^{2}(t_0^{[1]}(2)_*,t_0^{[1]}(2)))}(1_*)),3)\)

\(\alpha(400) = Q(t_0(t_0^{t_0^{Q(t_0(0),t_0(0))}(0)}(1_*)),3)\)

\(\alpha(500) = Q(t_0(t_0^{t_0^{Q^{2}(t_0(0)_*,t_0(0))}(0)}(1_*)),3)\)

\(\alpha(1000) = Q(t_0(t_0^{t_0^{t_0(1)}(0)}(1_*)),3)\)

\(\alpha(1500) = Q(t_0(t_0([2]1,2,0)),3)\)

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