Permutation? Relative Chaotic

[Leroy Quet]

I just submitted the following sequences:
(I editted the %Y-line of the first sequence here.)

>%S A118833 
>1,3,2,6,5,7,4,12,11,9,13,10,16,15,8,24,23,21,18,19,20,22,17,31,30,28,25,29
>,14,46
>%N A118833 a(1) = 1. a(n) = (|a(n-1)-n| +1)th positive integer which 
>doesn't occur earlier in the sequence.
>%C A118833 This sequence is likely a permutation of the integers.
>%e A118833 The first 8 terms of the sequence are 1,3,2,6,5,7,4,12. 
>|a(8)-9|+1 = 4, so a(9) = the 4th positive integer which doesn't occur 
>earlier in the sequence (ie. the 4th integer in the sequence 8, 9, 10, 11, 
>13, 14,..). Therefore a(9) = 11.
>%Y A118833 A118834
>%O A118833 1
>%K A118833 ,easy,more,nonn,

>%S A118834 1,3,2,7,5,4,6,15,10,12,9,8,11,29,14,13,23,19,20,21,18,22,17,16,27
>%N A118834 Inverse permutation of sequence A118833 (if A118833 indeed is a 
>permutation of the positive integers).
>%Y A118834 A118833
>%O A118834 1
>%K A118834 ,easy,more,nonn,

Even though there is some definite order to the sequences, they do seem 
to act somewhat chaotically.

1) Are these sequences definitely permutations of the positive integers?
(I suspect this is easy to prove.)

2) Is there a closed form representation which (non-recursively) gives 
each term's value?
(I suspect this is harder, but not impossible, to find.)
 
n's where a(n) = n form the sequence: 1, 5, 22,...

n's where a(n-1) = n form the sequence: 3, 7, 15, 29,...

If a(n-1) = n, then a(n) = : 2, 4, 8, 14,...

Are any of these last 3 sequences in the EIS? (Each brings up many hits 
with the few terms given.)


tthanks,
Leroy Quet