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Alexey Ustinov
  • 12.3k
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  • 87
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Numerical results give random picture.

ListPlot[Table[FractionalPart[Sqrt[PartitionsP[i]]], {i, 1, 5000}]]

enter image description here

Alexey Ustinov
  • 12.3k
  • 7
  • 87
  • 119