2-surprising sequences etc

[N. J. A. Sloane]

Dear Seqfans,

the latest issue of Scientific American (Dec 2003), page 122,
has a column by D E Shasha about surprising sequences

could someone look into this and see if there are
sequences that should be added to the OEIS?

for example,  what about:

Number of 2-surprising binary sequences of length n
Number of 3-surprising binary sequences of length n
...
Number of 2-surprising ternary sequences of length n
...

and

Length of longest 2-surprising sequence with n different symbols.
Length of longest 3-surprising sequence with n different symbols.
...

I did not investigate - these may be boring, or they may already
be in the OEIS under another name. But they look interesting,
and possibly surprising.

NJAS