[seqfan] Re: Is this sequence identical to A062802?

[Felix Fröhlich]

Thank you all for the replies and the editing of A062802.

Regards
Felix

2015-08-15 1:36 GMT+02:00 Neil Sloane <njasloane at gmail.com>:

> I added that as a question to A062802.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Aug 14, 2015 at 1:06 PM, APPLEGATE, DAVID L (DAVID L) <
> david at research.att.com> wrote:
>
> > I see - I misunderstood Felix's criteria.  I read "sequence of successive
> > digit sums" as meaning digit sums of prefixes of the number, not as
> > iterated digit sums.
> >
> > -David
> >
> > -----Original Message-----
> > From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Max
> > Alekseyev
> > Sent: Thursday, August 13, 2015 4:14 PM
> > To: Sequence Fanatics Discussion list
> > Subject: [seqfan] Re: Is this sequence identical to A062802?
> >
> > A062802(5) does satisfy Felix's criteria.
> > I believe that Felix's sequence and A062802 coincide. I double there is a
> > simple proof for that, but heuristically it is very plausible.
> > If they do not match and Felix's sequence has prime p not matching a(n),
> > then p < a(n) but sumdigits(p) > sumdigits(a(n)), and furthermore
> > sumdigits(p) itself passes Felix's criterion. The later implies that
> > sumdigits(p) is likely significantly larger than sumdigits(a(n)), which
> is
> > an obstacle for the existence of such p.
> >
> > Regards,
> > Max
> >
> >
> > On Thu, Aug 13, 2015 at 4:00 PM, APPLEGATE, DAVID L (DAVID L) <
> > david at research.att.com> wrote:
> >
> > > No, it's not the same.  As noted in the comment on A062802, a(5) is
> > > known and given, and does not satisfy the criteria for this sequence.
> > > It is also not equal to A103830 for a similar reason.
> > >
> > > -David
> > >
> > > -----Original Message-----
> > > From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Felix
> > > Fröhlich
> > > Sent: Thursday, August 13, 2015 3:33 PM
> > > To: Sequence Fanatics Discussion list
> > > Subject: [seqfan] Is this sequence identical to A062802?
> > >
> > > Dear Sequence fans,
> > >
> > > I've been thinking about the following sequence:
> > >
> > > Smallest prime p where the sequence of successive digit sums contains
> > > exactly n distinct primes other than p.
> > >
> > > The following PARI code generates terms of this sequence:
> > > dsumpnum(n) = s=n; i=0; while(#Str(s) > 1, s=sumdigits(s);
> > > if(ispseudoprime(s), i++)); i
> > > a(n) = p=2; while(dsumpnum(p)!=n, p=nextprime(p+1)); p
> > >
> > > The initial four terms of this sequence are 2, 11, 29, 2999 (with
> > > offset 0). The next term appears to be (relatively) large.
> > >
> > > Now what I've been wondering about is this:
> > >
> > > Is this sequence the same as A062802? If yes, is there an easy proof
> > > or, if no, an easy disproof?
> > >
> > > Best regards,
> > > Felix
> > >
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