The meaning of the related numbers

Question: What follows in the sequence below?

10233432943

As a hint, I must say I do not like the single 1 in it. It is unclear if the sequence even started with 1, but the 1 it needed.

I had to resolve my annoyance with 1 somehow and did that by removing ones from related numbers. Below the list of improved numbers:
7,3,9,3,3,6505537,233432943

Answer:

1 (aaarg, that ridiculous number again)

Please tell me what the related numbers represent.

Hints about hints.

The weak one.

The strong one.

For now I think I said enough about this hint

The backward one.

The strong hint, part two

The backward hint explained