RosettaCodeData/Task/Juggler-sequence/Mathematica/juggler-sequence.math

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next[n_Integer] := If[EvenQ@n, Floor[Sqrt[n]], Floor[n^(3/2)]]
stats[n_Integer] :=
Block[{data = Most@NestWhileList[next, n, # > 1 &], mx},
mx = First@Ordering[data, -1];
{n, Length[data], data[[mx]], mx - 1}]
{TableForm[Table[stats@n, {n, 20, 39}],
TableHeadings -> {None, {"n", "length", "max", "max pos"}}]