[seqfan] a(n)+[the a(n)th digit of S] is prime

[Eric Angelini]

Hello SeqFans,
Term "a" + the "a"th digit of the seq S  is prime;
S was extended with the smallest available integer
not yet in S and not leading to a contradiction;
S = 1,3,2,5,6,7,40,11,20,10,17,21,23,24,65,16,18,31,60,35,200,38,39,44,30,...

Example:
1+the 1st digit of S = 1+1=2
3+the 3rd digit of S = 3+2=5
2+the 2nd digit of S = 2+3=5
5+the 5th digit of S = 5+6=11
6+the 6th digit of S = 6+5=11
7+the 7th digit of S = 7+4=11
40+the 40th digit of S = 40+3=43
...
(the 40th digit of S starts "39" at the end of the seq above).

Remark:
S will stop when it will need one of the terms of http://oeis.org/A124584
--> "Primes p such that q-p >= 10, where q is the next prime after p."

Question:
Could we forbid the terms of A124584 to make S infinite?
Best,
É.