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

Graeme McRae graememcrae at gmail.com
Fri Sep 13 07:44:24 CEST 2013


Do you agree with me that if you require that all the mth ratios also be
integers, and also be strictly increasing, you get A058891, which is
2^(2^(n-1)-1)? If so, Jon, you might want to cross-reference the two
sequences, and put a comment in A058891 to that effect, because I don't see
such a comment there already.

--Graeme McRae
Palmdale, CA


On Thu, Sep 12, 2013 at 9:08 PM, Graeme McRae <graememcrae at gmail.com> wrote:

> 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
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> ______________________________**_________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>



More information about the SeqFan mailing list