[seqfan] Re: More terms are required for A218976

[Charles Greathouse]

> Making it by successive divisions (as ordinarily one might get it)
consumes too much time.

This really isn't the bottleneck. It takes 1.25 divisions, on average,
which is pretty cheap.

The problem is that it has to (in most cases) check every number between
a(n-1) and a(n) to find a(n), and to check each possible k to a large
bound. Reducing this bound would be very helpful.

A significant constant factor could be saved if this 'obvious' conjecture
were proved:
Either a(n) = a(n-1) + 1 or a(n) = 1 mod 5.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Tue, Nov 20, 2012 at 5:52 PM, Remy José Cano Ramírez <
aallggoorriitthhmmuuss at gmail.com> wrote:

> 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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