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<blockquote type=cite cite><font size=3><br>
At 10:47 PM 10/10/2002 +0100, Neil Fernandez wrote:<br>
<blockquote type=cite cite>Continuing the 'differences between perfect
powers' theme, I've just<br>
submitted these:<br>
..........................................<br>
<br>
perfect powers for which the three closest perfect powers are
smaller:<br>
36, 144, 2209 (no others <10^5)<br>
..........................................</blockquote></blockquote><br>
I wrote:<br>
<br>
<br>
<blockquote type=cite cite>I get <br>
36,144,2209,1664100,1685159,1906624,8000000,10077696,10556001,<br>
12117361,25411681,28629151,52521875,67108864,134217728,387420489<br>
</blockquote><br>
<br>
<br>
Whoops, I had a bad bug! I get:<br>
<br>
(corrected) 36,144,2209,6436369<br>
<br>
<br>
<blockquote type=cite cite><blockquote type=cite cite>perfect powers for
which the two closest perfect powers are greater:<br>
25, 121, 2187 (no others <10^5)<br>
..........................................</blockquote><br>
<br>
I get:<br>
<br>
25,121,2187,1860867,4084101,7880599,9765625,11316496,24010000,<br>
33554432,60466176,244140625</blockquote><br>
(corrected) 25,121,2187,6431296,6434856<br>
<br>
<br>
<blockquote type=cite cite><blockquote type=cite cite>As for:<br>
<br>
perfect powers for which the four closest perfect powers are
smaller:<br>
(no terms <10^5)</blockquote><br>
<br>
I get:
1664100,1685159,10077696,10556001,28629151,67108864,134217728</blockquote><br>
(corrected) - none < 2,100,000,000.<br>
<br>
<br>
<br>
<br>
<blockquote type=cite cite><blockquote type=cite cite>perfect powers for
which the three closest perfect powers are greater:<br>
(no terms <10^5).</blockquote><br>
<br>
I get: 60466176</blockquote><br>
(corrected) - none < 2,100,000,000.<br>
<br>
Sorry for the error. :-(<br>
<br>
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<div>+---------------------------------------------------------+</div>
<div>| Jud
McCranie
|</div>
<div>|
|</div>
<div>| Programming Achieved with Structure, Clarity, And Logic |</div>
<div>+---------------------------------------------------------+</div>
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