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

[Max Alekseyev]

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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