[1] Aballion = f{10}{10} = 10
[2] Abellion = f{100}{10} = 1092
[3] Abillion = f{1,000}{10} = 10992
[4] Abollion = f{10,000}{10} = 109,992
[5] Abullion = f{100,000}{100} = 1099,902
[6] Acallion = f{1,000,000}{100} = 10999,902
[7] Acellion = f{10,000,000}{1,000} = 109,999,002
[8] Acillion = f{100,000,000}{1,000} = 1099,999,002
[9] Acollion = f{1,000,000,000}{10,000} = 10999,990,002
[10] Acullion = f{10,000,000,000}{10,000} = 109,999,990,002
[11] Adallion = f{100,000,000,000}{100,000} = 1099,999,900,002
...
[96] Azallion = f{1 Untrigintillion}{100 Quattuordecillion} ~ 101 Untrigintillion, nearly googolplex
...
[100] Abogoogol = f{10 Duotrigintillion}{10 Quindecillion} ~ 1010 Duotrigintillion
...
[192] Azagoogol = f{1 Tresexagintillion}{100 Trigintillion} ~ 101 Tresexagintillion
Beta Regiment
Members: 1920
[193] Aballionplex = Aballion# = 1010
[194] Abellionplex = Abellion# = 1010↑92
[195] Abillionplex = Abillion# = 1010↑992
[196] Abollionplex = Abollion# = 1010↑9,992
...
[384] Azagoogolplex = Azagoogol# = 1010↑(10↑192)
[385] Aballionduplex = Aballion#2 = 1010↑10
[386] Aballiontriplex = Aballion#3 = 1010↑(10↑10)
...
[393] Aballioncentiplex = Aballion#10 = 1010↑(10↑(10↑(10↑10↑(10↑(10↑(10↑(10↑10))))))
[394] Abellionduplex
...
[2112] Azagoogolcentiplex = Azagoogol#10
Gamma Regiment
Members: 9
[2113] Babaion = f{10, 100}(100)=(2✕googolgoogol-98)↑googol-9910
[2114] Baboion = f{10, 100}(10) = (2✕googolgoogol-8)↑googol-910
[2115] Bacaion = f{10, 100}(1) = (2✕googolgoogol+1)↑googol10
[2116] Bacoion = f{10, 100}(0.1) = (2✕googolgoogol+1.9)↑googol+0.910
[2117] Badaionbit = 1010 billion
[2118] Super-Badaionbit = 2 badaionbits↑2 badaionbits-1 10
[2119] Ultra-Badaionbit = 2 googolplex↑2 googolplex-1 10
[2121] Badaion = f{10, 10, 100}(10) = f{super-badaionbit, ultra-badaionbit} (1090)
Whatever. To be honest, I’m getting kind of bored now making all these numbers, but I hope you understand just how big you can go.
2-entry level
[1] Million = {10, 6}
[2] Billion = {10, 9}
[3] Minigol (10 billion) = {10, 10}
[4] Googol (10 duotrigintillion) = {10, 100}
[5] Supergol (10 duotrigintatrecentillion) = {10, 1000}
[6] Ultragol = {10, 10000}
[7] Kilogol = {10, 100000}
[8] Hypergol = {10, {10, 6}}
...
[40] Googolplex = {10, {10, 100}}
[93] Zottagol = {10, {10, 257}}
3-entry level
[94] Super-terragol = {10, 6, 2}
[95] Super-petagol = {10, 7, 2}
[96] Super-exagol = {10, 8, 2}
[97] Super-zettagol = {10, 9, 2}
[98] Super-yottagol = {10, 10, 2}
[99] Super-xovagol = {10, 11, 2}
[100] Super-weicagol = {10, 12, 2}
[101] Super-wundagol = {10, 13, 2}
...
[110] Super-entagol = {10, 22, 2}
...
[175] Super-zottagol = {10, 87, 2}
[176] Super-googolplex = {10, 100, 2}
...
[261] Zottagolplex = {10, 87, 3}
[262] Super-googolduplex = {10, 100, 3}
...
[347] Zottagolduplex = {10, 87, 4}
...
[1036] Super-googolcentiplex = {10, 100, 12}
...
[1121] Zottagolcentiplex = {10, 87, 13}
4-entry level
[1122] Millionsuperplex = {10, 6, 1, 2} = {10, 5, million}
[1123] Minigolsuperplex = {10, 10, 1, 2} = {10, 9, minigol}
[1124] Millionultraplex = {10, 60, 1, 2} = {10, 59, novemdecillion}
[1125] Minigolultraplex = {10, 100, 1, 2} = {10, 99, googol} = googolsuperplex
[1126] Googolultraplex = {10, 1000, 1, 2} = {10, 999, kilogol}
[1127] Millionhyperplex = {10, 6, 1, 3} = {10, 4, millionsuperplex}
[1128] Minigolhyperplex = {10, 10, 1, 3} = {10, 8, minigolsuperplex}
[1129] Millionsuperhyperplex = {10, 60, 1, 3} = {10, 58, millionultraplex}
[1130] Minigolsuperhyperplex = {10, 100, 1, 3} = {10, 98, minigolultraplex} = googolhyperplex
[1131] Googolsuperhyperplex = {10, 1000, 1, 3} = {10, 998, googolultraplex}
[1132] Millionultrahyperplex = {10, 6, 1, 4} = {10, 3, millionhyperplex}
[1133] Minigolultrahyperplex = {10, 10, 1, 4} = {10, 7, minigolhyperplex}
[1134] Googolultrahyperplex = {10, 100, 1, 4} = {10, 97, minigolsuperhyperplex}
Getting bored again.