[seqfan] Is this sequence identical to A062802?

[Felix Fröhlich]

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