[seqfan] Re: slowest-growing "accelerating" sequence

[Graeme McRae]

I calculated the same numbers. So it's certainly possible, but not likely
we both goofed in our calculations. It's more likely that we both
misunderstood the definition, I suppose. My calculation works by making a
running tally of the mth ratios, and then to find each new element of the
sequence, a(n+1) I take the product of the previous element a(n) and all of
the most recently calculated mth ratios, add 1, and take the floor. So I
say, it's time for you to submit the Jon Wild sequence.

superseq-reply at oeis.org
8:59 PM (4 minutes ago)

Report on [ 1,2,5,16,68,404,3587,51747,1343181]:
Many tests are carried out, but only potentially useful information
(if any) is reported here.

Content is available under
The OEIS End-User License Agreement: http://oeis.org/LICENSE


Even though there are a large number of sequences in the OEIS, at least
one of yours is not there! If it is of general interest, please submit it
using the submission form http://oeis.org/Submit.html
and it will (probably) be added!  Thanks!

--Graeme McRae
Palmdale, CA


On Thu, Sep 12, 2013 at 8:21 PM, Jon Wild <wild at music.mcgill.ca> wrote:

>
> Hard to believe this is new--is it right?
>
> a(n) = 1,2,5,16,68,404,3587,51747,**1343181,70863530...
>
> Seems more likely that I've calculated this wrong than that no one has
> thought of it before and put it in the oeis: a(n) is the slowest growing
> integer sequence beginning with 1 whose sequences of mth-order quotients
> are all strictly increasing, for all values of m.
>
> (explanation by example in case it isn't clear: the 1st-order quotients
> relate successive elements of the sequence; they are 2, 2.5, 3.2, 4.25, ...
>  The 2nd-order quotients are 1.25, 1.28, ... 3rd-order quotients are 1.024,
> etc. These, and all successive mth-order sequences, are strictly
> increasing. So in a sense, the sequence is increasing, its rate of increase
> is increasing, the rate of its rate of increase is increasing, ad
> infinitum--and a(n) is the slowest sequence for which this is true.)
>
> jon wild
>
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