$ jq -n -r -f Self_referential_sequence.jq
The maximal length to convergence for seeds up to 1000000 is 21.
The corresponding seeds are the allowed permutations
of the representative number(s): 9900
For each representative seed, the self-referential sequence is as follows:
Representative: 9900
Self-referential sequence:
[
  9900,
  2920,
  192210,
  19222110,
  19323110,
  1923123110,
  1923224110,
  191413323110,
  191433125110,
  19151423125110,
  19251413226110,
  1916151413325110,
  1916251423127110,
  191716151413326100,
  191726151423128100,
  19181716151413326000,
  19182716151423128000,
  29181716151413330000,
  19281716151423230000,
  19281716151413430000,
  19182716152413230000
]