Re: What is the approximating density of this sequence?

In article <4368a7d1$0$96612$892e7fe2@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
MuTsun Tsai <don.tsai@xxxxxxxxxxxxxx> wrote:
>http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A061383
>
>Any help will be appreciated.

I.e. consider the set S of positive integers x such that the arithmetic mean of the base-10
digits of x is an integer. You want the asymptotic density,
d = lim_{n -> infty} |S intersect {1..n}|/n.

A number of m digits is in S if and only if the sum of its digits is divisible by m.
Thus every m'th m-digit number is in S. Since 1/m -> 0 as m -> infty, the
asymptotic density is 0.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada





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