It is not even known that all digits appear

**infinitely often**," Wagon remarks.This definition appears somewhat frequently and is found in the following Acronym Finder categories:

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It is not even known that all digits appear **infinitely often**," Wagon remarks.

In this note, we show that the ratio of consecutive values Z(n)/Z(n-1) and Z(n)/Z(n+1) are unbounded; that Z(2n)/Z(n) is unbounded; and that n=Z(n) takes every integer value **infinitely often**.

However, no one knows whether all of the digits from 0 to 9 appear **infinitely often** in this expansion or whether one-tenth of the digits are ones, and so on.