Permutations based on themselves

[Leroy Quet]

I just submitted the following permutations of the positive integers:

>%S A118315 1,2,3,4,6,5,9,7,12,8,16,10,17,11
>%N A118315 a(1)=1. a(2n)= lowest positive integer not occurring among the 
>earlier terms of the sequence. a(2n+1) = the a(n)th positive integer among 
>those positive integers not occurring earlier in the sequence. 
>%C A118315 Sequence is a permutation of the positive integers.
>%e A118315 For a(9) we want the a(4)th = 4th positive integer among those 
>not equal to any of the first 8 terms of the sequence (those positive 
>integers not equal to 1,2,3,4,6,5,9, or 7). Among those positive integers 
>not equal to any the first 8 terms (which is the sequence  
>8,10,11,12,13...), 12 is the 4th. So a(9) = 12.
>Now for a(10) we want the lowest positive integer that does not occur 
>among the first 9 terms of the sequence. So a(10) = 8.
>%Y A118315 A118316,A118317,A118318
>%O A118315 1
>%K A118315 ,easy,more,nonn,

>%S A118316 1,2,3,4,6,5,8,10,7,12,14,9
>%N A118316 Inverse permutation of sequence A118315.
>%C A118316 Sequence is a permutation of the positive integers.
>%Y A118316 A118315,A118317,A118318
>%O A118316 1
>%K A118316 ,easy,more,nonn,

>%S A118317 1,2,3,5,4,8,6,12,7,13,9,19
>%N A118317 a(2n-1)= lowest positive integer not occurring among the 
>earlier terms of the sequence. a(2n) = the a(n)th positive integer among 
>those positive integers not occurring earlier in the sequence. 
>%C A118317 Sequence is a permutation of the positive integers.
>%e A118317 For a(8) we want the a(4)th = 5th positive integer among those 
>not equal to any of the first 7 terms of the sequence (those positive 
>integers not equal to 1,2,3,5,4,8, or 6). Among those positive integers 
>not equal to any the first 7 terms (which is the sequence  
>7,9,10,11,12,13...), 12 is the 5th. So a(8) = 12.
>Now for a(9) we want the lowest positive integer that does not occur among 
>the first 8 terms of the sequence. So a(9) = 7.
>%Y A118317 A118315,A118316,A118318
>%O A118317 1
>%K A118317 ,easy,more,nonn,

>%S A118318 1,2,3,5,4,7,9,6,11,13
>%N A118318 Inverse permutation of sequence A118317.
>%C A118318 Sequence is a permutation of the positive integers.
>%Y A118318 A118315,A118316,A118317
>%O A118318 1
>%K A118318 ,easy,more,nonn,

(It should be noted that A118318 is different than A102399.)

Is there a direct way to calculate the nth terms of any of these 
sequences? (Something involving the highest power of 2 dividing n, 
perhaps?)

thanks,
Leroy Quet