[SequencesForFun] Re: The OEIS will be on holiday for the rest of the year!

[cino hilliard]

Hi Kerry and Fans,

>From: Kerry Mitchell <lkmitch at gmail.com>
>To: seqfan at ext.jussieu.fr
>Subject: Re: [SequencesForFun] Re: The OEIS will be on holiday for the rest 
>of the year!
>Date: Fri, 6 Jan 2006 13:49:20 -0700
>
Kerry Mitchell wrote:
>I think some heuristic like this would be helpful; I am not a mathematician
>nor do I study sequences professionally, so I'm not sure what would be
>considered important in the "real world."  I'm willing to admit that none 
>of
>the sequences I've submitted are important, but they were interesting to me
>when I was studying them for fun.  Any other objective measures of
>importance that someone can offer for guidance?
>Kerry

>Cino Hilliard wrote:
>This helps. Context. A sequence to be important must have at least 1 other
> > context in the data base before submit. Doing advanced searches on text 
>in
> > you definition would help find other
> > contexts if you are not sure of your creation. I can do that.
> >

I think another criterion would be if you can make a meaningful conjecture 
from or about the
sequence. This will not necessarily make it important or interesting to all 
readers but to more
readers than just the sequence and definition.

Also it may be interesting how you came up with the sequence. Eg., in a 
dream, at work, the news,
a movie etc. This would imply you are not "contriving." I often come up with 
concoctions not
important nor interesting to many to find out about 90% of the time the 
sequence is already out
there. Eg., I came up with the sequence 0,1,2,3,4,7,10,11,12,14... which I 
gleaned from a
crossword puzzle clue: mce mce mce. This turned out to be "three blind 
mice." Eureka! I submitted the idea with numbers to find it out there as 
IBAN numbers. Nevertheless, if similar reasoning does
yeild an unknown sequence, I would classify it as interesting. Important? 
No.

Then on the other hand I do come up with some goodies. The only "nice" 
sequences I have ever
come up with were already in the data base. It is interesting in this 
re-invention process we find
different ways to generate an existing sequence. I think sequences like that 
are interesting.

So that may be another criterion before submitting: can I generate it in 
another way? Here we will
quickly see that "two heads are better than one."  Still, a thught.

Consider:0,1,2,3,4,6,12 The first term without repetition of the core 
sequences in the database. Is
this an important sequence? I don't think so.

Some keyword frequency stratistics through Part 114 of the database

Keyword     number of sequences
-------------    ---------------------------------
Unkn               18
Dumb              60
Core              133
Obsc              156
Eigen             259
Word             296
Bref               341
Dead             631
Mult              740
Tabf              839
Uned             967
Frac             1273
Full              2073
Hard            2438
Fini              2954
Cofr             3533
Cons            3693
Tabl             4136
More            5691
Nice             6049
Sign             6908
Base           16173
Core and Nice 124

So there we have it. 133 core or important sequences in the database and 124 
that are both core
and nice. The first lexically core and nice sequence is

0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0, 
A000035 core,easy,nonn,nice,mult A simple periodic sequence.

Have fun and a nice and core new year,
Cino