[seqfan] More terms are required for A218976

Remy José Cano Ramírez aallggoorriitthhmmuuss at gmail.com
Tue Nov 20 23:52:41 CET 2012


Would someone be interested in the following problem?...

The A218976 entry at OEIS has few terms, due mainly to it lacks of a better
algorithm for generating correct terms than the basic definition of the
sequence and its testing by trial and error.

But, I noticed something interesting about this sequence:

Let be x[i] an element of a table for the first M positive integers. A
candidate for being accepted as an A218976 term would be tested against
each one of the M entries at the described table in order to verify if the
definition of A218976 is satisfied.

In order to meet this goal, we need the 5-adic valuation of each entry in
the table. Making it by successive divisions (as ordinarily one might get
it) consumes too much time. Due to such disadvantage, a replacement
computation is needed there (if possible).

My current proposal for replacement is something quite different to the
Maple program shown there: In some way, a good deal of combinatorial
structure becomes evident if the successively-repeated outcome frequency is
counted on the differences between the quantities

( floor(x[i]/20) + floor(x[i]/5) )

And

 valuation(x[i], 5)

For a wide enough table. My personal goal is at least 1000 terms before Jan
1st 2013. But it might be possible only after identified the proper
algorithm. For now, I am calling what I found "The forty roses gardener
algorithm", but for not prevent anyone from having the pleasure of watching
it, I decided omit more specific details here . The first step of an
algorithmic characterization of the data previously described, is easy to
catch. The rest of the algorithm is the challenge part where I am sure that
would need some help. Below is my e-mail address for contact.

And all the best.

Sincerely,

R. J. Cano, <remy at ula.ve>


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