Do "easy" sequences appear more often?

[simone at cs.york.ac.uk]

Dear Seqfans,

It is a fact that certain mathematical objects seem to show up very often
(see, e.g., Doron Zeilberger "Opinion 49: Why Ubiquity is so Ubiquitous",
http://www.math.rutgers.edu/~zeilberg/Opinion49.html). A plausible reason
could be that frequent objects are "easy".

Together with two cognitive psychologists, Demis Basso and Laura Pieroni,
I am designing some psychological tests involving integer sequences.

In the experiments we need a set of six sequences s_1,...,s_6 with the
following properties:

The sequences s_1,s_2,s_3 appear very often;

The sequences s_4,s_5,s_6 appear very rarely (so far, at least), but s_1
"looks similar to" s_4,...,s_3 "looks similar to" s_6.

The notion of similarity is not formal here, but nonetheless it should be
clear.

Would you please indicate me six "good" sequences with the above properties?

Please, email me directly, unless you think that your answer looks
interesting to the other Seqfans.

Thanks for your time.

Simone

http://www-users.york.ac.uk/~ss54