[seqfan] a(a(n) + n) is prime

[Eric Angelini]

Hello SeqFans,
am I wrong or this seq is not in the OEIS yet?

S = 1,2,3,5,4,7,8,6,11,9,10,12,13,17,19,14,15,16,23,29,31,18,20,37,21,41,22,24,25,43,47,53,26,59,...

S is build with those rules:
     . a(1)=1
     . a(a(n)+n) is prime
     . S is extended with the smallest integer not yet in S and not leading to a contradiction.

We see here, that:
a(1)+1 -> 1+1=2 -> a(2) which is prime [2]
a(2)+2 -> 2+2=4 -> a(4) which is prime [5]
a(3)+3 -> 3+3=6 -> a(6) which is prime [7]
a(4)+4 -> 5+4=9 -> a(9) which is prime [11]
a(5)+5 -> 4+5=9 -> a(9) which is prime [11]
a(6)+6 -> 7+6=13 -> a(13) which is prime [13]
a(7)+7 -> 8+7=15 -> a(15) which is prime [19]
a(8)+8 -> 6+8=14 -> a(14) which is prime [17]
a(9)+9 -> 11+9=20 -> a(20) which is prime [29]
...

n = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
S = 1,2,3,5,4,7,8,6,11,9,10,12,13,17,19,14,15,16,23,29,31,18,20,37,21,41,22,24,25,43,47,53,26,59,...
sum 2 4 6 9 9 1 1 1  2 1 21 24 26 31 34 30 32 ...
              3 5 4  0 9

I guess S is a permutation of the Naturals.
Primes appear in S in their natural order.
Best,
É.