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<div>Dear seqfans,</div>
<div>I think this curious fact deserves your attention:</div>
<div><br></div>
<div><font face="Courier New" size="+2" color="#000000"><b>ID
Number:</b> A064770<br>
<b>Sequence: </b>
0,1,1,1,2,2,2,2,2,3,10,11,11,11,12,12,12,12,12,13,10,11,11,<br>
<b> </b>
11,12,12,12,12,12,13,10,11,11,11,12,12,12,12,12,13,20,21,21,<br>
<b> </b>
21,22,22,22,22,22,23,20,21,21,21,22,22,22,22,22,23,20,21,21,<br>
<b> </b>
21,22,22,22,22,22,23<br>
<b>Name: </b> Replace each digit of n by
the floor of its square root.<br>
<b>Example: </b> 26 -> [1.414...][2.449...] -> 12, so
a(26) = 12.<br>
<b>Keywords: </b> base,nonn,nice,new<br>
<b>Offset: </b> 0</font></div>
<div><font face="Courier New" size="+2"
color="#000000"><b>Author(s):</b> Santi Spadaro (spados@katamail.com),
Oct 19 2001</font></div>
<div><br></div>
<div>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:</div>
<div><br></div>
<div><br></div>
<blockquote type="cite"
cite>http://www.seqfan.net/spadaro/A064770-1.gif</blockquote>
<blockquote type="cite"
cite>http://www.seqfan.net/spadaro/A064770-2.gif</blockquote>
<div><br>
<br>
</div>
<div>For further explorations here's the Mathematica code:</div>
<div><br></div>
<div>f[n_] := Floor[Sqrt[n]]</div>
<div>k[n_] := Map[f, IntegerDigits[n]]</div>
<div>ndig[a_, b_] := 10a + b</div>
<div>tonum[dig_] := Fold[ndig, 0, dig]</div>
<div>j = Table[tonum[k[n]], {n, 1, 100}]</div>
<div>ListPlot[j]</div>
<div><br></div>
<div>Change 100 in the 5th line with 10^k k=3,4,5,6,7... and see what
happens.</div>
<div><br></div>
<div><br>
<br>
</div>
<div>Best Wishes,</div>
<div>Santi Spadaro<br>
</div>
<div><br></div>
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