[seqfan] FW: Re: Sums of each ten terms of A033308

Jeremy Gardiner jeremy.gardiner at btinternet.com
Mon Jan 11 08:26:44 CET 2010


------ Forwarded Message
From: zak seidov <zakseidov at yahoo.com>
Date: Sun, 10 Jan 2010 19:45:31 -0800 (PST)
To: Jeremy Gardiner <jeremy.gardiner at btinternet.com>
Subject: Re: [seqfan] Re: Sums of each ten terms of A033308

Yes, I think that this is the base 10 related sequence.
In all positional systems such "periodicity" should take place.
And "period length" is also base-related.
And primeness is not a necessary precondition.
Still this is interesting sequence
(for those who is interested in it for course ;)))

What is the period length for other bases?
Anyone wish to check it?
My guess: for base b=37 (e.g.) it should be
A000217(b)=b(b+1)/2 =703.

Thanks, Zak


--- On Sun, 1/10/10, Jeremy Gardiner <jeremy.gardiner at btinternet.com> wrote:

> From: Jeremy Gardiner <jeremy.gardiner at btinternet.com>
> Subject: Re: [seqfan] Re: Sums of each ten terms of A033308
> To: "zak seidov" <zakseidov at yahoo.com>
> Date: Sunday, January 10, 2010, 5:22 PM
> Zak,
> 
> I don't think the periodicity has to do with these being
> primes - for
> example I find a similar periodicity for the positive
> integers (see test
> program below).
> 
> Perhaps it's a feature of a positional number system...
> Although not to say
> it isn't interesting!
> 
> Regards,
> Jeremy Gardiner 
> 
> rem sum of digits of integers taken k at a time
> rem Chipmunk BASIC v3.6.4(b8)
> k=10
> s$=""
> for n=1 to 8000
> s$=s$+str$(n)
> next n
> j=1
> z=len(s$)-k
> do
> s=0
> for i=j to j+k-1
> s=s+val(mid$(s$,i,1))
> next i
> print s
> j=j+k
> if j>z then goto xxx
> loop
> xxx:
> close #1
> end
> 
> 
> On 9/1/10 12:15, "zak seidov" <zakseidov at yahoo.com>
> wrote:
> 
> > This is the first and evident choice -
> > but sure you may look for any other base.
> > 
> > And do you know the answer to my Q plz?
> > 
> > --- On Sat, 1/9/10, Jeremy Gardiner <jeremy.gardiner at btinternet.com>
> wrote:
> > 
> >> From: Jeremy Gardiner <jeremy.gardiner at btinternet.com>
> >> Subject: [seqfan] Re: Sums of each ten terms of
> A033308
> >> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> >> Date: Saturday, January 9, 2010, 3:36 AM
> >> 
> >> Why groups of 10? What happens with other
> partitions?
> >> 
> >> On 9/1/10 07:53, "zak seidov" <zakseidov at yahoo.com>
> >> wrote:
> >> 
> >>> Take A033308 Decimal expansion of
> Copeland-Erdos
> >> constant:concatenate primes:
> >>> 
> >>> 
> >> 
> 
2,3,5,7,1,1,1,3,1,7,1,9,2,3,2,9,3,1,3,7,4,1,4,3,4,7,5,3,5,9,6,1,6,7,7,1,7,3,7>>
> ,
> >>> 9,8,3,8,9,9,7,1,0,1,...
> >>> 
> >>> Partition it in groups of 10 and write down
> sums of
> >> each group:
> >>> p10 =
> >>
> 31,40,45,54,47,23,29,35,44,41,51,24,38,35,51,38,26,38,53,...
> >>> Graph of p10 shows some misterious
> (quasi-)periodicity
> >> of length about 50:
> >>>   Is it real? Any explanation?
> >>> 
> >> 
> >> 
> >> 
> >> 
> >> _______________________________________________
> >> 
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >> 
> > 
> > 
> > 
> 
> 
> 




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