Trooga- is an extension to the booga- function created by means of name extrapolation, interpreting the letter "b" as a shortened version of "bi" and replacing it with "tr-" for "tri".[1]

It is defined as follows:

trooga(n) = boogan(n) (exponent indicates recursion)

It has growth rate \(\omega + 1\) in the fast-growing hierarchy, meaning it is about as powerful as Graham's function.

Below are some examples:

trooga(1) = booga(1) = 1

trooga(2) = booga(booga(2)) = booga(4) = 4444

trooga(3) = booga(booga(booga(3))) = booga(booga(27)) = booga(27{25}27) = (27{25}27){27{25}27 - 2}(27{25}27)

trooga(4) = booga4(4) = booga3(4444) ~> 4{4{4{4444 - 2}4}4}4

trooga(64) >Graham's number.

trooga(googol)=bed.

Sources

Googological affixes

Suffixes: -teen · -ty · -plex · -illion · -yllion · -exian · -chime · -toll · -gong · -bong · -throng · -illiob
Prefixes: gar- · fz- · fuga- · megafuga- · booga- · trooga- · googo- · googolple-
SI prefixes: deca- · hecto- · kilo- · mega- · giga- · tera- · peta- · exa- · zetta- · yotta-
Obsolete SI prefixes: myria-
Extended SI prefixes: 666 · 105 · 107 · 1027 · 1030 · 1033 · 1036 · 1039 · 1042 · 1045 · 1048 · 1051 · 1054 · 1057 · 1060 · 1063 · 1066 · 1069 · 1072 · 1075 · 1078 · 1081 · 1084 · 1087 · 1090 · 10100 · 10120 · 10150 · 10180 · 10210 · 10240 · 10270 · 10300 · 10600 · 10900 · 101200 · 101500 · 101800 · 102100 · 102400 · 102700 · 103000 and higher

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