[seqfan] Doubly self-describing sequence: a(n) = prime integer and prime digit position in S

[Eric Angelini]

... and to elaborate on my last post, we could build P in which every a(n)
    would "say":
- the a(n)th integer of P is prime
- the a(n)th digit of P is prime
and where a(n) is chosen to be the smallest positive number not already in P
and not leading to a contradiction.

I guess P starts like this (computed by hand):

P = 2,3,5,1,7,8,23,11,20,15,29,14,22,37,31,19,20,21,53,41,43,59,47,...

P diverges quite quickly from A121053 - "A sequence S describing the position
of its prime terms" http://oeis.org/A121053
2, 3, 5, 1, 7, 8, 11, 13, 10, 17, 19, 14, 23, 29, 16, 31, 37, 20, 41, 43, 22, 47, 53, 25, 59, 27, 61, 30, 67, 71, 73, 33, 79, 35, 83, 38, 89, 97, 40, 101,...

Best,
É.