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Re: Plotting a function -

  • To: mathgroup at
  • Subject: [mg71691] Re: Plotting a function -
  • From: "Ray Koopman" <koopman at>
  • Date: Sun, 26 Nov 2006 05:49:31 -0500 (EST)
  • References: <ek990u$k88$>

Craig Reed wrote:
> Hi -
> I'm trying to get Mathematica 5.2 to graph a function which is the ratio of
> integers which have a '3' in them. Done in Exce3l, the graph of the first
> 32,000 data points has a fractal look to it, especially when done with a
> log scale.
> What I've tried is the following
> f[x_] := Boole[DigitCount[x, 10, 3]]
> g[x_] := Sum[f, {i, x}]/x
> Plot[g, {x, 1, 100}]
> I get 3 errors of "g is not a michine-size real number at" followed by 3
> real numbers:
> 1.000004125
> 5.016125.....
> 9.39607.....
> What am I doing wrong?  or perhaps what I should ask is, "Is there a better
> way?"

If f[x] is supposed to give a numeric indicator of whether or not the
decimal representation of an integer 'x' has a '3' in it, then try

f[x_Integer] := Boole@MemberQ[IntegerDigits@x,3]

If the numerator of g[x] is supposed to be the number of values
in the range 1,...,x for which f gives '1', then you could say

g[x_Integer] := Sum[f[i], {i, x}]/x

There are other ways to get g, some of which may be much faster
but less obvious.

To get the plot you could do


Again, there are other ways to do it, but this is clearest.

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