A121760/1: two (interesting?) sequences

[Jonathan Post]

Exceptions that prove the rule, being both "base" and "nice":

 A014417 <http://www.research.att.com/%7Enjas/sequences/A014417>
 Representation of n in base of Fibonacci numbers.
 A030101 <http://www.research.att.com/%7Enjas/sequences/A030101>
 a(n) is the number produced when n is converted to base 2, reversed and
then converted back to base 10.
 A039724 <http://www.research.att.com/%7Enjas/sequences/A039724>
 Numbers in base -2.
 A099542 <http://www.research.att.com/%7Enjas/sequences/A099542>
 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).
 A037888 <http://www.research.att.com/%7Enjas/sequences/A037888>
 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.
 A037183 <http://www.research.att.com/%7Enjas/sequences/A037183>
 Smallest number which is palindromic (with at least 2 digits) in n bases.
 A048986 <http://www.research.att.com/%7Enjas/sequences/A048986>
 Home primes in base 2: primes reached when you start with n, and (working
in base 2) concatenate its prime factors
(A048985<http://www.research.att.com/%7Enjas/sequences/A048985>);
repeat until a prime is reached (or -1 if no prime is ever reached). Answer
is written in base 10.
 A068505 <http://www.research.att.com/%7Enjas/sequences/A068505>
 Value of n interpreted in base (b+1), where
b=A054055<http://www.research.att.com/%7Enjas/sequences/A054055>(n)
is the largest digit in decimal representation of n.
 A005352 <http://www.research.att.com/%7Enjas/sequences/A005352>
 Numbers n such that base -2 representation for -n read as binary number.
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.


On 8/21/06, Ralf Stephan <ralf at ark.in-berlin.de> wrote:
>
> >I'd read many messages here that "base"
> >seqs are mostly non-interesting,
> >but never undestood why, sorry.
>
> Do you read math papers, Zak? If so, then you have certainly
> experienced the feeling that a specific entity, say a sequence,
> has connections to things you didn't think of before. This happens
> regularly with interesting sequences, and I guess I'm not alone
> in having made the experience that this doesn't happen with base
> sequences. That's why we say they're not interesting.
>
> But what is, for example? Everything in combinatorics, count on it,
> will appear sooner or later in other fields like physics, IT, biology
> and more, so combinatorial sequences are certainly the most interesting
> in the OEIS. But there's more, and you get only a feel if you read
> the literature.
>
>
> Regards,
> ralf
>
>
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