[seqfan] Working demo and webpage

[Robert Munafo]

Introducing *Sloandora* (I couldn't help it :-), a rough but working
proof-of-concept.

I have published a description of my system at mrob.com/pub/math/sloandora

Here is a demo. The user creates a topic "egypt" and seeds it with an
Egyptian Fraction related sequence:

bash$ ./Sloandora
                    _                  _
                   (_` |  _  ._  ._   _|  _  ._ ._
                   , ) | ( ) ,-| | | ( | ( ) |  ,-|
                    ~  ~  ~  `~` ~ ~  ~`  ~  ~  `~`

           User-Aided Integer Sequence Auto-Discovery System
             by Robert Munafo, with the seqfan list members

Loading database index...
Select a topic: egypt
There is no topic 'egypt'.
Do you want to create one? yes
Enter the A-number of a sequence to start this topic: A100140
Rating 'A100140' with strength 1 ................''''''''''''''''
Next recommendation: A117116 (score 0.181495)
Denominators of an Egyptian Fraction for phi = (1+sqrt(5))/2.

Command loop (type 'help' for help)
Topic 'egypt' > relevant
Rating 'A117116' with strength 1 ................''''''''''''''''
Next recommendation: A006525 (score 0.422316)
Denominator of Egyptian fraction for e-2.
Topic 'egypt' > show
Current sequence is A006525, and its score is 0.422316 :
%---- A006525

%I M1553
%S 2,5,55,9999,3620211523,25838201785967533906,
%T 3408847366605453091140558218322023440765
%N Denominator of Egyptian fraction for e-2.
%H <a href="http://www.research.att.com/~njas/sequences/Sindx_Ed.html#Egypt">Index
entries for sequences related to Egyptian fractions</a>
%H Eric Weisstein's World of Mathematics, <a href="
http://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%Y Adjacent sequences: A006522 A006523 A006524 this_sequence A006526 A006527
A006528
%Y Sequence in context: A114029 A013171 A073422 this_sequence A042161
A101151 A030244
%K nonn
%O 0,1
%A njas
%E More terms from H. P. Robinson.


Topic 'egypt' > y
Rating 'A006525' with strength 1 ................''''''''''''''''
Next recommendation: A006524 (score 0.798684)
Egyptian fraction for 1/ Pi.
Topic 'egypt' > A001234
Loading A001234 (current score: 0.34579)
Stirling numbers of first kind.
Topic 'egypt' > ?
Sloandora commands:

  Show                 Display the entire record for the current sequence
  Y, Relevant          The currently displayed sequence matches this topic
  N, Irrelevant        The currently displayed sequence does NOT match
  Next, Skip           Show me another sequence you think is relevant
  A012345              Show me sequence A012345
  Best                 Re-select the latest recommendation
  Quit, Exit, Bye      Exit Sloandora
  Help, ?              Displays this help

Topic 'egypt' > best
Current recommendation: A006524 (score 0.798684)
Egyptian fraction for 1/ Pi.
Topic 'egypt' > y
Rating 'A006524' with strength 1 ................''''''''''''''''
Next recommendation: A006487 (score 1.147965)
Egyptian fraction for square root of 2.
Topic 'egypt' > q
Saving topic 'egypt'...done

I did another test starting with a "Mandelbrot" sequence, A052154. It
recommended A098403 and A054671, both of which I rated "relevant".
   Then it recommended A054670, A055544, and A090037, all of which I rated
"irrelevant".
   Then it recommended A102525, A006874, A006875, and A006876, all of which
I rated "relevant" because they are Mandelbrot-related.

So it basically works, at least for the two cases I tried (-: but obviously
many improvements are needed, as discussed earlier. The comments from Rick
so far are relevant, and are mostly addressed in the literature (see the
academic references to get an idea for how such systems can be optimized).

Using the techniques used in established systems, combined with new metadata
or "category tags" added to the database (as already suggested by several
others), this system could be improved significantly.


I want to thank Rick Shepherd for the idea. It is the fulfillment of two
long-term desires I have always wanted to fulfill (implementing something
that uses a concordance metric, and obtaining a more useful way to search
the OEIS). Even if no-one else likes it, I'm going to keep it (-:

-- 
 Robert Munafo  --  mrob.com