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

[Neil Sloane]

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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> >
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> >
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> >
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