Digits of Hyperfactorial and Barnes G

n

23

remove trailing zeros

base

10

BarnesG

Hyperfactorial

This Demonstration shows a histogram counting the digits of BarnesG or Hyperfactorial in any base.

The built-in Mathematica function Hyperfactorial is defined as the product of elements in the self-counting sequence

1,2,2,3,3,3,4,4,4,4,…

, so

H(n)

n

∏

k=1

k

. The built-in Mathematica function BarnesG is defined as the product of the factorials of consecutive integers,

G(n)

n-2

∏

k=1

k!

. The number of digits in the elements of these sequences grow quadratically, as does the number of trailing zeros.