$Line = 0;

s = 0; f = 15000; m = 1; n = 24; gstep = 5;
initplot = 
        ListPlot[ContinuedFraction[Tan[1] + m/n, f], PlotRange -> All, 
          Prolog -> PointSize[1/150], 
          GridLines -> {Automatic, Automatic}];

ss = 10000; ff = 15000; ptsize = 150;
Show[initplot, PlotRange -> {{ss, ff}, {0, 2500}}]

countseq = 
        Drop[ContinuedFraction[Tan[1] + m/n, ff], ss - 1];

Table[i, {i, gstep, f, gstep}], Table[i, {i, 5, 250, 5}]

Length[{1294, 1, 1, 1, 1, 1, 19, 1, 1, 1, 3, 1, 1, 2, 19, 1, 9, 1, 1, 
        1, 80, 1, 1, 1, 9, 1, 19, 2, 4, 1, 4, 1, 19, 1, 1, 3, 1, 1, 326, 5, 
        2, 1, 19, 1, 3, 3, 1, 3, 20, 4, 1, 1, 2, 1, 81, 2, 1, 10, 20, 2, 4, 
        1, 4, 1, 19, 1, 2, 1, 5275, 4, 20, 2, 1, 1, 3, 1, 1, 1, 20, 32, 82, 
        1, 3, 1, 1, 3, 20, 2, 4, 1, 4, 1, 19, 1, 14, 1, 331, 1, 4, 3, 20, 1, 
        1, 15, 1, 1, 20, 2, 1, 10, 83, 2, 7, 2, 20, 2, 4, 1, 4, 1, 20, 8, 
        1342, 1, 6, 1, 20, 7, 8, 1, 20, 6, 2, 2, 83, 1, 9, 1, 1, 1, 20, 2, 4, 
        1, 4, 1, 20, 3, 4, 1, 337, 1, 14, 1, 20, 3, 1, 3, 3, 1, 20, 2, 7, 2, 
        84, 1, 1, 2, 5, 1, 20, 2, 4, 1, 4, 1, 20, 2, 21871, 2, 20, 1, 8, 7, 
        21, 3, 1, 1, 3, 1, 85, 32, 21, 2, 4, 1, 4, 1, 20, 1, 2, 5, 344, 1, 1, 
        3, 1, 1, 21, 64, 21, 1, 1, 2, 5, 1, 85, 1, 2, 1, 1, 4, 21, 2, 4, 1, 
        4, 1, 20, 1, 6, 1, 1390, 8, 21, 1, 1, 1, 3, 1, 1, 2, 21, 2, 2, 6, 87, 
        6, 2, 2, 21, 2, 4, 1, 4, 1, 21, 16, 350, 1, 2, 5, 21, 1, 3, 3, 1, 3, 
        21, 1, 2, 1, 1, 4, 87, 1, 5, 2, 1, 1, 21, 2, 4, 1, 4, 1, 21, 4, 5659, 
        1, 2, 1, 21, 2, 1, 1, 3, 1, 1, 1, 21, 1, 1, 7, 1, 1, 88, 3, 1, 1, 3, 
        1, 21, 2, 4, 1, 4, 1, 21, 2, 3, 2, 356, 3, 4, 1, 21, 1, 1, 15, 1, 1, 
        21, 1, 5, 2, 1, 1, 88, 1, 30, 1, 21, 2, 4, 1, 4, 1, 21, 1, 1, 1, 1, 
        1, 1438, 2, 1, 2, 22, 7, 8, 1, 21, 1, 1, 1, 9, 1, 89, 2, 2, 6, 22, 2, 
        4, 1, 4, 1, 21, 1, 4, 3, 362, 2, 3, 2, 22, 3, 1, 3, 3, 1, 21, 1, 30, 
        1, 90, 10, 1, 2, 22, 2, 4, 1, 4, 1, 21, 1, 93630, 1, 21, 1, 8, 7, 22, 
        1, 3, 1, 1, 3, 91, 1, 1, 7, 1, 1, 22, 2, 4, 1, 4, 1, 22, 5, 2, 1, 
        368, 16, 23, 64, 23, 10, 1, 2, 92, 4, 1, 1, 2, 1, 22, 2, 4, 1, 4, 1, 
        22, 2, 1, 2, 1486}]

maxbase = 80; Lenght[countseq]
ct = Table[Count[countseq, i], {i, 1, maxbase}]; 
    MatrixForm[Transpose[{Table[i, {i, 1, maxbase}], ct}]]