[seqfan] A flagpole sequence of itself (word)

[Eric Angelini]

Hello SeqFans,
a little word sequence not (yet?) in the OEIS:

                             |
                             |
  1                          O N E
  7                  S E V E N 
  3                    T H R E E
  6                          S I X
  5                    F I V E
 11                    E L E V E N
  8                          E I G H T
  9                          N I N E
  2                          T W O
 13                        T H I R T E E N
  4                    F O U R
 10                        T E N
 12                      T W E L V E
 16                          S I X T E E N
 15                        F I F T E E N
 26          T W E N T Y S I X
 14                          F O U R T E E N
 18                        E I G H T E E N
 17                      S E V E N T E E N
 19                    N I N E T E E N
 20                      T W E N T Y
111    O N E H U N D R E D E L E V E N
 21                      T W E N T Y O N E
 25          T W E N T Y F I V E
 22                      T W E N T Y T W O
 23                    T W E N T Y T H R E E
 24                      T W E N T Y F O U R
 26            T W E N T Y S I X
 28          T W E N T Y E I G H T
 30                        T H I R T Y
 27                          T W E N T Y S E V E N
 29                    T W E N T Y N I N E
 etc.                        I
                             N
                             E
                             T
                             W
                             O
                             |
                             |
                             |
                             |
(explanation: the "single letter column" above the
four "|", here (the "flagpole"), spells vertically
O N E S E V E N ... which is the sequence itself).
In extending the sequence, always try to use the 
smallest Natural not yet present in the sequence.

Is the sequence a permutation of the Naturals?

Best,
É.
(there is a follow-up post coming with numbers only)