Skipping & moving up/down by primes

[Leroy Quet]

I just submitted the following sequence to the OEIS:

>%S A000001 1,3,6,11,2,16,29,10
>%N A000001 a(1) = 1; Skipping over integers occurring earlier in the 
>sequence, count down p(n) (p(n) = nth prime) from a(n) to get a(n+1). If 
>this is <= 0, instead count up from a(n) p(n) positions (skipping 
>already occurring integers) to get a(n+1).
>%C A000001 If we did not skip earlier occurring integers when counting, we 
>would instead have Cald's sequence (A006509).
>%e A000001 The first 5 terms of the sequence can be plotted on the number 
>line as:
>1,2,3,*,*,6,*,*,*,*,11,*,*,*,*,*.
>Now, a(5) is 2. Counting p(5) = 11 down from 2 gets a negative integer. So 
>we instead count up 11 positions -- skipping the 3, 6, and 11 as we count 
>-- to arrive at 16 (which is at the right-most * of the number-line above).
>%Y A000001 A091023,A091263,A006509
>%O A000001 1
>%K A000001 ,more,nonn,


Question: Is this a permutation of the positive integers?

If so, could someone calculate/submit the inverse permutation sequence?

thanks,
Leroy Quet