## FANDOM

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Not to be confused with Ackermann ordinal.

The Ackermann numbers are a sequence defined using arrow notation as:[1]

$A(n) = n\underbrace{\uparrow\uparrow...\uparrow\uparrow}_nn$

where $$n$$ is a positive integer. The first few Ackermann numbers are $$1\uparrow 1 = 1$$, $$2\uparrow\uparrow 2 = 4$$, and $$3\uparrow\uparrow\uparrow 3 =$$ tritri. More generally, the Ackermann numbers diagonalize over arrow notation, and signify its growth rate is approximately $$f_\omega(n)$$ in FGH and $$g_{\varphi(n-1,0)}(n)$$ in SGH.

The $$n$$th Ackermann number could also be written $$3$$Template:Mathlink$$n$$ or $$\lbrace n,n,n \rbrace$$ in BEAF.

The Ackermann numbers are related to the Ackermann function; they exhibit similar growth rates, although their definitions are quite different.

## Last 10 digits Edit

Below are the last few digits of the first ten Ackermann numbers.

• 1st = 1
• 2nd = 4
• 3rd = ...2,464,195,387 (tritri)
• 4th = ...0,411,728,896 (tritet)
• 5th = ...8,408,203,125 (tripent)
• 6th = ...7,447,238,656 (trihex)
• 7th = ...1,565,172,343 (trisept)
• 8th = ...6,895,225,856 (trioct)
• 9th = ...7,392,745,289 (trienn)
• 10th = ...0,000,000,000 (tridecal)

## Sources Edit

1. Ackermann Number