Googology Wiki
Googology Wiki
Googology Wiki
38,256
pages
in: Numbers, Bignum Bakeoff contestant, Computers,
and 2 more

ioannis.c

Sign in to edit

View full site to see MathJax equation

ioannis.c is an entry "Ioannis" submitted to Bignum Bakeoff.[1] The code defines a function similar to the Ackermann function, defines a single-argument function using it, and iterates that function.

The output is exactly booga- prefix applied 116 times to 9 and can be calculated as s(116) using s(k+1) = s(k){s(k)-2}s(k) (where arrow notation is used) and starting with s(0) = 9.

The output is then approximately equal to \(f_{\omega+1}(115)\), which is larger than Graham's number. In fact it is larger than \(G_{115}\), while Graham's number is only \(G_{64}\). It is also slightly larger than corporal and graatagold.

Code[]

int a(int k,int m,int n)
{if (k==1) return(m+n);
else {if (n==1) return m;
else return a(k-1,m,a(k,m,n-1));}}
#define d(n) a(n,n,n)
int main(void)
{return d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(
d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(
d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(
d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(d(
d(d(d(d(d(d(d(d(9)))))))))))))))))))))))))))))))))))))))
))))))))))))))))))))))))))))))))))))))))))))))))))))))))
)))))))))))))))))))));}

Approximations[]

Notation Approximation
Bowers' Exploding Array Function {9,116,1,2}
Chained arrow notation 9→9→116→2
Hyper-E notation E115##115#115
Strong array notation s(9,116,2,2)
Fast-growing hierarchy \(f_{\omega+1}(115)\)
Hardy hierarchy \(H_{\omega^{\omega+1}}(115)\)
Slow-growing hierarchy \(g_{\Gamma_0}(115)\)

Sources[]

  1. ↑ http://djm.cc/bignum-results.txt

See also[]

Large numbers in computers
Community content is available under CC-BY-SA unless otherwise noted.