# [seqfan] Re: Primes arising in Newman digit sums

Thu Nov 18 16:05:16 CET 2010

```Paul Hanna informed me that link
http://www.hinduwi.com/jornals/ijmms/2008/908045html
seems to be broken.

Another simple possibility is to find in Google cite "Generalized Newman Phenomena and Digit Conjectures on Primes".

Regards,

----- Original Message -----
From: Vladimir Shevelev <shevelev at bgu.ac.il>
Date: Thursday, November 18, 2010 15:35
Subject: [seqfan] Re: Primes arising in Newman digit sums
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> Dear Charles,
>
> Your question is open and very difficult. In the same paper, M.
> Drmota and M. Skalba proved for Newman sum
> S_{m,0}(x)=Sum{0<=n<x, n==0 (mod m)} (-1)^s(n),
> where s(n)=A000120(n),
> that if m is multiple of 3, then S_{m,0}(x)>0 for x>=x_0.
> Note that an estimate of x_0(m) is also a difficult problem.
> Using method of trigonometrical sums, I
> in paper http://www.hinduwi.com/jornals/ijmms/2008/908045html ,
> in particular, get an algorithm
> for such estimates. As an example, I found that if m=21, then
> x_0(21)<e^{909}.
> Best regards,
> ----- Original Message -----
> From: Charles Greathouse <charles.greathouse at case.edu>
> Date: Wednesday, November 17, 2010 18:43
> Subject: [seqfan]  Primes arising in Newman digit sums
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>
> > Consider sequence A131342: Primes arising in Newman digit
> > sums.  The comment
> >
> > %C A remarkable result of M. Drmota and M. Skalba: the only
> > primes p
> > =< 1000 satisfying S_p,0(n) > 0 (at least for sufficiently
> > large n)
> > are 3, 5, 17, 43, 257, 683.
> >
> > taken from
> > http://arXiv.org/pdf/0709.3821
> >
> > seems to suggest that the sequence should be finite and full
> > (and also
> > base).  But instead it has keyword:more.  Do I
> > misunderstand a special
> > case for the general one (in which case the sequence, I hope,
> > can be
> > clarified), or are the keywords wrong?
> >
> > Charles Greathouse
> > Analyst/Programmer
> > Case Western Reserve University
> >
> >
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> >
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> >
>