[net.math] Yet another thought

jcz (07/23/82)

	Here is an interesting bit I just thought of, it might not be
     new, but readers of this list may find it amusing to  think about.

		What numbers, in what ever base, describe their
		number of digits?

	e.g 10 (2) = 2 and has 2 digits.

	--jcz
	John Carl Zeigler

rjs (07/23/82)

The question was:

	What numbers, in what ever base, describe their number of
	digits?

Consider an n digit number in base b.  Its minimum value is b**(n-1).
For normal bases, b is an integer >= 2.  First note that b**(n-1) grows
much faster than n once n >= 2 and that b**(2-1)=b.  Thus the only
possible integer values for n are 1 and 2.  2 only works if b=2.
1 always works.

Robert Snyder		(harpo!floyd!rjs)

p.s. I'm not sure what numbers look like in bases other than integers
>= 2 (or if there is such a thing) so that's as far as I can pursue
this problem.