[seqfan] Re: 8/5 Sequence
Neil Sloane
njasloane at gmail.com
Tue Jun 12 18:50:49 CEST 2012
Yasutoshi, Thank you for posting that message.
You say there is something wrong with A082010.
The sequence looks correct to me, and so does
the related sequence A152199.
What exactly needs to be changed?
Neil
On Mon, Jun 11, 2012 at 5:01 AM, kohmoto <zbi74583.boat at orange.zero.jp>wrote:
> Hi, Neil and Seqfan
>
>
> I think A082010 is not correct. it and the sequence of definition are
> different.
> If you started from 0 then it must be the following.
> 0,1,2,1,2,....
>
> It is not so interesting.
> The first interesting case is the following.
>
>
> 3,5,9,15,25,41,66,33,53,85,137,220,110,55,89,143,229,367,588,294,147,236,118,59,95,153,245,393
>
> http://list.seqfan.eu/pipermail/seqfan/2009-September/009818.html
>
> Ask Don Reble.
> He has 2000000 terms of the sequence.
>
> Once Franklin wrote
> >This can be simplified: if x is odd, then next x is floor(8/5*x)+1.
> >No need for separate m and n; let r be the ratio (m/n), and if x is
> >odd, the next x is floor(r*x)+1. And now we don't even need r to be
> >rational.
>
>
> You are right.
> 8/5 sequence is one of the K-Sequence.
>
> a(n)=[A*a(n-1)+B]/p^m
> Where [N] is integer part of N, p^m is the highest p power dividing
> [A*a(n-1)+B]
>
> http://boat.zero.ad.jp/~zbi74583/ess0.htm
>
> 3 examples :
> See A028948, A029580, A036982
>
> >When r is the golden ratio, (sqrt(5)+1)/2, starting with 3, we get
> >A001595, a sequence of all odd numbers, so there is unlimited growth.
> >This may shed some light on what is happening with 8/5.
>
> I think your opinion is interesting.
> My observation is the following.
>
> p=2, a(0)=3, A=1.6, 1<=B<2
> In this area all sequences are unlimited.
>
> You say the case of A=(1+root(5))/2 is also unlimited.
> How did you find this fact?
> I think it is your discovery.
>
> Once I conjectured as follows.
>
> "K-Sequence which represents Fibonacci Sequence exists"
>
> I knew that A001959 is one of the K-Sequence.
> So my conjecture is almost right.
>
>
>
> Yasutoshi
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
--
Dear Friends, I have now retired from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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