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so I have a program that outputs a desired value for incrementing values of alpha. Right now, my program prints a list of these for 40 values of alpha in the form {alpha, newValue}.

d = 1000;
For[k = 1, k <= 40, k++,
  alpha = 0.1*k;
  fd = 3*d^2/(Pi^2);
   fs = fd*FareySequence[d];
  count = 0; 
  For[i = 1, i < fd, i++, 
   For[j = (i - 1), j > 0, j--, 
     If[(fs[[i]] - fs[[j]]) < alpha, count++, Break[]]];];
    newValue = count/d^2;
  Print["{", alpha, ",", newValue, "}"];
  ];

Here are the first few outputs:

{0.1,0}
{0.2,0}
{0.3,0}
{0.4,1911/100000}
{0.5,13593/250000}
{0.6,90521/1000000}
..
..
..
{3.9,1155653/1000000}
{4.,74163/62500}

I want to make a plot all of these outputs as coordinates. I want to plot these point on a graph with alpha on the x axis and newValue on the y axis. Any help would be appreciated.

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1 Answer 1

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Change the outer for loop to a table:

d = 1000;
sol = Table[alpha = 0.1*k;
fd = 3*d^2/(Pi^2);
fs = fd*FareySequence[d];
count = 0;
For[i = 1, i < fd, i++, 
For[j = (i - 1), j > 0, j--, 
If[(fs[[i]] - fs[[j]]) < alpha, count++, Break[]]];];
{k, count/d^2}, {k, 1, 40}];

ListPlot[sol]

gives the plot you're looking for!

enter image description here

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3
  • $\begingroup$ I'm getting an error "sol is not a list of numbers or pairs of numbers." $\endgroup$ Oct 17, 2020 at 15:08
  • $\begingroup$ @ NotSoTrivial I checked my code , it runs without error. Perhaps restart your session and try again ! $\endgroup$ Oct 17, 2020 at 15:12
  • $\begingroup$ Yes, thanks it works. The run time was just too long for large d. I also changed some of the parameters to make it a function of alpha. Thanks a lot! $\endgroup$ Oct 17, 2020 at 15:18

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