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

[APPLEGATE, DAVID L (DAVID L)]

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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