old sequences

[Brendan McKay]

A good partial solution to this problem is to have more
intelligence in the data base.  The source file will have
just the Fibonacci numbers, then the software around it will
automatically add  Fib(n) mod x, Fib(2n+1), etc, when a 
sequence is searched for.  The user can specify the degree
of effort that the search engine should be willing to put
into finding something matching the query.

Various degrees of cleverness are possible.  For example,
if given a sequence of 0 and 1 it will check if there is a
sequence in the database giving the required values mod 2.
If given a sequence containing only Fibonacci numbers but
not consecutively, it will look for a sequence f(n) such
that Fib(f(n)) is right, and if it can't find f(n) it
should report "I don't know what it is, but I noticed
there are only Fibonacci numbers in there".

[Aside: a search option that looks for sequences containing
a set of numbers but not in any particular order would be
easy to add and quite useful I think.]

I agree with JC that sequences like Fib(n) mod 9 should
definitely NOT go into the source file.  They are derived
sequences that should be deduced from the source file if
and when required.  This would make the database MORE
likely to identify a sequence, not less likely.

No, I didn't volunteer to write the software  :-).

Brendan.