[seqfan] Primes and digits

[Eric Angelini]

Hello SeqFans,

A155817 is the sequence S having the property that a(n) is the sum of the first a(n) digits of S itself.

What about a similar T sequence showing only prime numbers? 
I guess T would start:

T = 11,2,13,101,100207,31,41,10000100000003,103,1000117,61,113,1000000000000037,83,...
(the next prime would start with
"1" followed by at least 17 "0", if I didn't make prior errors -- which would be surprising :-((

Best,
É.