The Big Ass Number function is defined as \(\mathrm{ban}(n) = n^{^nn} = {}^{n + 1}n\), or nmegafuga(n).[1] In up-arrow notation, it can be expressed as \(n \uparrow (n \uparrow\uparrow n)\) or as \(n \uparrow\uparrow (n+1)\).

It was defined along with the Really Big Ass Number function by Matt Leach in a failed attempt to create an uncomputable function. In reality, the function's growth rate is around \(f_3(n)\) in the fast-growing hierarchy, nowhere close to the busy beaver function.

The first few values of \(\mathrm{ban}(n)\) are \(1, 16\), and \(3^{7,625,597,484,987}\), which has 3,638,334,640,025 decimal digits.

Sources Edit

  1. Really Big Numbers