[seqfan] Re: Primes arising in Newman digit sums

[Vladimir Shevelev]

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,
Vladimir


----- 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,
> Vladimir
> ----- 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
> > 
> > 
> > _______________________________________________
> > 
> > Seqfan Mailing list - http://list.seqfan.eu/
> > 
> 
>  Shevelev Vladimir‎
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/
> 

 Shevelev Vladimir‎