fractal-like plot

Santi Spadaro spados at
Fri Nov 2 20:48:02 CET 2001

Dear seqfans,
I think this curious fact deserves your attention:

ID Number: A064770
Sequence:  0,1,1,1,2,2,2,2,2,3,10,11,11,11,12,12,12,12,12,13,10,11,11,
Name:      Replace each digit of n by the floor of its square root.
Example:   26 -> [1.414...][2.449...] -> 12, so a(26) = 12.
Keywords:  base,nonn,nice,new
Offset:    0
Author(s): Santi Spadaro (spados at, Oct 19 2001

The plot of this sequence shows a curious (even if maybe not so 
surprising) fractal behaviour as you can see from the two plots 
(kindly hosted by Professor Gerard) in the links below:


For further explorations here's the Mathematica code:

f[n_] := Floor[Sqrt[n]]
k[n_] := Map[f, IntegerDigits[n]]
ndig[a_, b_] := 10a + b
tonum[dig_] := Fold[ndig, 0, dig]
j = Table[tonum[k[n]], {n, 1, 100}]

Change 100 in the 5th line with 10^k k=3,4,5,6,7... and see what happens.

Best Wishes,
Santi Spadaro

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