[seqfan] Is this seat available?

[Eric Angelini]

Hello SeqFans,
Here is a new idea to build a (silly) seq.
Start S with a(1)=1
The next integer we will "install" in S must be the smallest "uninstalled" yet; here "2":
This integer always tries to install itself in the first available place of S;
This place, here, is the one next to "1"; so "2" tries to "install" itself there;
S = 1, 2, ...
But "1" has a request: "If possible, install yourself "1" place away from me; if
this place is already occupied, then ok, you can install yourself next to me"; so:
S = 1, . , 2, ...
Now comes "3"; as it is impossible for "3" to install itself 1 place away from 1
(the place is taken by 2), "3" installs itself next to 1; so:
S = 1, 3, 2, ...
Now comes "4"; "4" tries to install itself next to "2" -- but "2" has a request: "If 
possible, install yourself "2" places away from me; if this place is already occupied, 
then ok, you can install yourself next to me"; so:
S = 1, 3, 2, . , . , 4, ...
Now comes "5" -- and "5" will be allowed to install itself next to "2" as "4" occupies
the place "5" should aim to; so:
S = 1, 3, 2, 5, . , 4, ...
Now comes "6" -- installing itself in the first available place, 5 places away from "5":
S = 1, 3, 2, 5, . , 4, . , . , . , 6, ...
Now comes "7" -- allowed to install itself next to 5; so:
S = 1, 3, 2, 5, 7 , 4, . , . , . , 6, ...
Now comes "8" -- installing itself "4" places away from "4"; so:
S = 1, 3, 2, 5, 7 , 4, . , . , . , 6, 8, ...
Now comes "9":
S = 1, 3, 2, 5, 7 , 4, 9 , . , . , 6, 8, ...
Now comes "10":
S = 1, 3, 2, 5, 7 , 4, 9 , . , . , 6, 8, . , . , . , . , . , 10, ...
Now comes "11":
S = 1, 3, 2, 5, 7 , 4, 9 , 11, . , 6, 8, . , . , . , . , . , 10, ...
Now comes "12":
S = 1, 3, 2, 5, 7 , 4, 9 , 11, . , 6, 8, . , . , . , . , . , 10, . , . , 12, ...
Now comes "13":
S = 1, 3, 2, 5, 7 , 4, 9 , 11, 13, 6, 8, . , . , . , . , . , 10, . , . , 12, ...

... and so on.
I get this start by hand:

S = 1,3,2,5,7,4,9,11,13,6,8,14,16,18,20,22,10,24,26,12,27,29,31,33,35,37,15,23,38,17,40,...

S is a permutation of the integers >0, of course.

Best,
É.