Self-junk

[Eric Angelini]

Hello SeqFan and Math-Fun,

Can someone find the last term of this (finite) sequence?

1 21 2 11 3 4 111 1122 5 6 7 8 9 22 23 22222 222222 2222222 22222222
222222222 24 25 26 222 27 28 29 32 33 34 35 36 37 38 39 42 43 44 45 46 47 48
49 52 53 54 55 56 57 58 59 62 63 64 65 66 667 68 69 72 2222 73 22223 74

Building rules:

1) The length of each integer is given by the succession
   of the digits of the sequence itself (first integers
   have length 1, 2, 1, 2, 1, 1, 3, ...)

2) No two identical integers in the sequence

3) When adding a new integer to the sequence, put always
   the smallest unused so far

4) Always have in mind that the final sequence must be as
   long as possible -- this explains why the above 8th integer
   is "1122" and not "1111", for instance: "1111" would block
   the sequence very fast:

   1 21 2 11 3 4 111 1111 5 6 7 8 9 -- stop, no more available
   integer of length "1"...

Best,
É.