From my experiments so far with n up to 2e10:
- The first missing value is tiny compared to the maximum observed number, so not much can be saved here.
- The observed numbers only cover 1/8 of the whole range, so we are dealing with a sparsely populated array in your proposal. This might not be the best way to store the sequence.
- The ratio of the maximum number to the sequence number is around 8:1 so not much to be gained here either.
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