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MathGroup Archive 2006

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Re: Plotting a function -

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71661] Re: Plotting a function -
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Sun, 26 Nov 2006 03:48:42 -0500 (EST)
  • References: <ek990u$k88$1@smc.vnet.net>

Although I am not quite sure that I understand your question, here is
one attempt.

However note that my solution is not very quick; I am sure someone else
will provide you with a better solution.

Clear["Global`*"]

Here is a function that checks if an integer contains 3 in base-10; if
so it returns 10, otherwise it returns 0.

f[x_Integer] := If[DigitCount[x, 10, 3] > 0, 1, 0]

E.g.

f /@ Range[100]
{0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0,
  1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}

Timing[f /@ Range[100000]][[1]]
5.984*Second

Here is your desired function (I believe!)

g[x_Integer] := Plus @@ N[f /@ Range[x]]/x

Here is your visualization

Timing[lst = g /@ Range[1000]][[1]]

32.09400000000001*Second

ListPlot[lst, PlotStyle -> {Blue, AbsolutePointSize[3]}, ImageSize ->
400, Axes -> False, Frame -> {True, True, False, False},
  FrameTicks -> {Range[0, 1000, 100], Range[0, 0.5, 0.1]}, PlotRange ->
{{-0.001, 1030}, {-0.001, 0.41}},
  Epilog -> Rectangle[{400, 0.1}, {800, 0.3}, ListPlot[Take[lst, 30],
PlotStyle -> {Blue, AbsolutePointSize[4]},
     DisplayFunction -> Identity]]]

Regards
Dimitris



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?"


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