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Booga- is a prefix used on a number n to indicate \(n\uparrow^{n-2}n\) or equivalently \(n\uparrow^{n-1}2\).[1] It may also be defined as "n n-ated to n" or equivalently "n n+1-ated to 2". The term was coined by Sbiis Saibian. It is equivalent to the sequence of Chihiro numbers, and is closely related to the Ackermann function and the Ackermann numbers. In Notation Array Notation, it can be expressed as \((n\{2,n-2\}n)\) or \((n\{2,n-1\}2)\).

Here are some examples:

  • booga(1) = 1 + 1 = 2
  • booga(2) = 2 × 2 = 4
  • booga(3) = 33 = 27
  • booga(4) is equal to 4444 or 44 or 4↑↑4, the famous megafuga(4).
  • booga(5) = 5↑↑↑5 = 55555
  • ...
  • booga(googolplex) is called boogagoogolplex.

Pseudocode Edit

function hyper(a, b, n):
    if n = 1:
        return a + b
    result := b
    repeat b - 1 times:
        result := hyper(result, b, n)
    return result

function booga(n):
    return hyper(n, n, n)

Sources Edit

  1. The Fz, The Fuga & The Megafuga

See also Edit

Googological affixes

Suffixes: -teen · -ty · -plex · -illion · -yllion · -chime · -toll · -gong · -bong · -throng
Prefixes: gar- · fz- · fuga- · megafuga- · booga-
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 · 1090 · 10100 · 10120 · 10150 · 10180 · 10210 · 10240 · 10270 · 10300 · 10600 · 10900 · 101200 · 101500 · 101800 · 102100 · 102400 · 102700 · 103000 and higher


Numbers named with the fuga- family of prefixes

Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · gargoogol · gargoogolplex
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fzeleven · fztwenty · fzhundred · fzgoogol · fzmillion · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugaeleven · megafugatwelve · megafugathirteen · megafugafourteen · megafugafifteen · megafugasixteen · megafugaseventeen · megafugaeighteen · megafuganineteen · megafugatwenty · megafugathirty · megafugaforty · megafugafifty · megafugasixty · megafugaseventy · megafugaeighty · megafuganinety · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex
Booga-: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaseven · boogaeight · booganine · boogaten · boogahundred · boogagoogol · boogagoogolplex