# [seqfan] Re: Another surprising omission from OEIS

Charles Greathouse charles.greathouse at case.edu
Fri Nov 13 14:53:21 CET 2009

```I'm quite in agreement, Alonso.  Base-2 sequences (represented in base
10, of course) are frequently quite natural.

Generalizing my concern about base-dependent sequences, I don't like
arbitrariness in sequences. One thing that can bother me about a
sequence is its apparent arbitrariness.  "Numbers that are palindromic
in base 7 and repdigits in base 12" has two apparently arbitrary bases
and two apparently unrelated concepts (repdigit and palindrome).  It
would bother me less if there were some connection between
(different-base) repdigits and palindromes, or if the choice of base
was somehow natural ("Comments: 7 is the lowest base in which
palindromes have the foo property, which allows repunits in any
coprime base to be ..." -- this would reduce the 'degrees of freedom'
in some vague sense from 3 to 1).  A167389 is a real example of this:
though not base-dependent, it seems to be an entirely arbitrary
function
(argument(exp(-(ln(2)+W(n,-(1/2)*ln(2)))/ln(2)))*ln(2)+Im(W(n,-(1/2)*ln(2))))/(2*Pi*ln(2))
As always, I'm not sure whether the sequence is dull enough to be
excised, just another uninteresting sequence, or interesting but
lacking a motivating comment.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Thu, Nov 12, 2009 at 4:17 PM, Alonso Del Arte
<alonso.delarte at gmail.com> wrote:
> As I wrote my previous message, sequences about base 2 were in the back of
> my mind, and I thought "Maybe I should say something about them," so I say
> it now: Their importance in computer applications alone more than justifies
> their study. The number-theoretic study of powers of two also occasionally
> benefits from considering the binary representation of the applicable
> numbers.
>
> On the other hand, something like "Numbers that are palindromic in base 7
> and repdigits in base 12" (a contrived example) I wouldn't care about at
> all. But my lack of interest does not mean that such a sequence will or will
> not be of interest to anyone besides the submitter. If I see a base uned
> sequence that I can fix up, I will, even if I can't see the point of it.
> It's not my place to rule on whether such sequences should or should not be
> in the OEIS.
>
> AL
>
> On Thu, Nov 12, 2009 at 3:33 PM, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:
>
>> With all the insults thrown at 'base' sequences in this thread, I want to
>> defend base-2 'base' sequences.
>> Unlike base-10, base 2 is more "natural", since it is often times the
>> smallest-order base that is interesting.
>>
>> And then there are the applications of some base-2 sequences to computer
>> science.
>>
>> Still, I may have inadvertently used the 'base' keyword for some of my
>> binary-based sequences which are more simply defined by non-base means, a
>> no-no according to an earlier post to this thread.
>>
>> Thanks,
>> Leroy Quet
>>
>>
>> [ ( [ ([( [ ( ([[o0Oo0Ooo0Oo(0)oO0ooO0oO0o]]) ) ] )]) ] ) ]
>>
>>
>>
>>
>>
>>
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```