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Visualize Sequences
Visualize sequences using DiscretePlot for direct insight into behavior.
In[1]:=

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GraphicsGrid@

 Partition[

  Table[DiscretePlot[f, {k, 50}, 

    PlotLabel -> f], {f, {Mod[k, 11], Mod[k^2, 11], Mod[k^3, 11], 

     Mod[11^k, 9], BitLength[k], DigitCount[k, 2, 1], EulerPhi[k], 

     DivisorSigma[0, k], DivisorSigma[1, k]}}], 3]
Out[1]=