Exceptions that prove the rule, being both "base" and "nice":<br>
<br>
<table border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr><td align="left" valign="top" width="100"><a href="http://www.research.att.com/%7Enjas/sequences/A014417" title="Representation of n in base of Fibonacci numbers.">A014417</a></td>
<td width="5"><br>
</td>
<td align="left" valign="top">
Representation of n in base of Fibonacci numbers.</td></tr></tbody>
</table>
<br>
<table border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr><td align="left" valign="top" width="100"><a href="http://www.research.att.com/%7Enjas/sequences/A030101" title="a(n) is the number produced when n is converted to base 2, reversed and then converted back to base 10.">
A030101</a></td>
<td width="5"><br>
</td>
<td align="left" valign="top">
a(n) is the number produced when n is converted to base 2, reversed and then converted back to base 10.</td></tr></tbody>
</table>
<br>
<table border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr><td align="left" valign="top" width="100"><a href="http://www.research.att.com/%7Enjas/sequences/A039724" title="Numbers in base -2.">A039724</a></td>
<td width="5"><br>
</td>
<td align="left" valign="top">
Numbers in base -2.</td></tr></tbody>
</table>
<br>
<table border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr><td align="left" valign="top" width="100"><a href="http://www.research.att.com/%7Enjas/sequences/A099542" title="Rhonda numbers to base 10. An integer n is a Rhonda number to base b if the product of its digits in base b equals b*Sum of prim">
A099542</a></td>
<td width="5"><br>
</td>
<td align="left" valign="top">
Rhonda numbers to base 10. An integer n is a Rhonda number to base b if
the product of its digits in base b equals b*Sum of prime factors of n
(including multiplicity).</td></tr></tbody>
</table>
<br>
<table border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr><td align="left" valign="top" width="100"><a href="http://www.research.att.com/%7Enjas/sequences/A037888" title="a(n)=(1/2)*Sum{|d(i)-e(i)|} where Sum{d(i)*2^i} is base 2 representation of n, and e(i) are digits d(i) in reverse order.">
A037888</a></td>
<td width="5"><br>
</td>
<td align="left" valign="top">
a(n)=(1/2)*Sum{|d(i)-e(i)|} where Sum{d(i)*2^i} is base 2
representation of n, and e(i) are digits d(i) in reverse order.</td></tr></tbody>
</table>
<br>
<table border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr><td align="left" valign="top" width="100"><a href="http://www.research.att.com/%7Enjas/sequences/A037183" title="Smallest number which is palindromic (with at least 2 digits) in n bases.">A037183</a></td>
<td width="5"><br>
</td>
<td align="left" valign="top">
Smallest number which is palindromic (with at least 2 digits) in n bases.</td></tr></tbody>
</table>
<br>
<table border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr><td align="left" valign="top" width="100"><a href="http://www.research.att.com/%7Enjas/sequences/A048986" title="Home primes in base 2: primes reached when you start with n, and (working in base 2) concatenate its prime factors (A048985); re">
A048986</a></td>
<td width="5"><br>
</td>
<td align="left" valign="top">
Home primes in base 2: primes reached when you start with n, and (working in base 2) concatenate its prime factors (<a href="http://www.research.att.com/%7Enjas/sequences/A048985" title="Working in base 2, replace n by the concatenation of its prime divisors in increasing order (write answer in base 10).">
A048985</a>); repeat until a prime is reached (or -1 if no prime is ever reached). Answer is written in base 10.</td></tr></tbody>
</table>
<br>
<table border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr><td align="left" valign="top" width="100"><a href="http://www.research.att.com/%7Enjas/sequences/A068505" title="Value of n interpreted in base (b+1), where b=A054055(n) is the largest digit in decimal representation of n.">
A068505</a></td>
<td width="5"><br>
</td>
<td align="left" valign="top">
Value of n interpreted in base (b+1), where b=<a href="http://www.research.att.com/%7Enjas/sequences/A054055" title="Largest digit of n.">A054055</a>(n) is the largest digit in decimal representation of n.</td>
</tr></tbody>
</table>
<br>
<table border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr><td align="left" valign="top" width="100"><a href="http://www.research.att.com/%7Enjas/sequences/A005352" title="Numbers n such that base -2 representation for -n read as binary number.">A005352</a></td>
<td width="5"><br>
</td>
<td align="left" valign="top">
Numbers n such that base -2 representation for -n read as binary number. </td></tr></tbody>
</table>
<br>
and 630 others. So one asks, why are these base sequences nice
and others not? Typically, it is indeed because of inherent
mathematical structure, or illumination of the base notation itself, or
unexpected iterative behavior, though that list is not exhaustive.<br>
<br><br><div><span class="gmail_quote">On 8/21/06, <b class="gmail_sendername">Ralf Stephan</b> <<a href="mailto:ralf@ark.in-berlin.de">ralf@ark.in-berlin.de</a>> wrote:</span><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
>I'd read many messages here that "base"<br>>seqs are mostly non-interesting,<br>>but never undestood why, sorry.<br><br>Do you read math papers, Zak? If so, then you have certainly<br>experienced the feeling that a specific entity, say a sequence,
<br>has connections to things you didn't think of before. This happens<br>regularly with interesting sequences, and I guess I'm not alone<br>in having made the experience that this doesn't happen with base<br>sequences. That's why we say they're not interesting.
<br><br>But what is, for example? Everything in combinatorics, count on it,<br>will appear sooner or later in other fields like physics, IT, biology<br>and more, so combinatorial sequences are certainly the most interesting
<br>in the OEIS. But there's more, and you get only a feel if you read<br>the literature.<br><br><br>Regards,<br>ralf<br><br></blockquote></div><br>