[seqfan] Set operations (was Re: binary expansion 1+0*)

[franktaw at netscape.net]

A quick survey of 100 random sequences (using WebCam) found that 61 
were (or appeared to be) sets in increasing order, 3 were sets, but not 
in order, and 36 were not sets. (I didn't count, but perhaps a dozen of 
the non-sets failed to be sets only by repetition of 2 or more zeros at 
the start.)

That doesn't leave much room for a majority of the OEIS to represented 
by set operations from some core. My guess would be that no more than 
about 10% can be so defined, maybe significantly less.

Franklin T. Adams-Watters

-----Original Message-----
From: Charles Greathouse <charles.greathouse at case.edu>

More generally, I wonder how many sequences can be defined as A union
B, A intersect B, or A setminus B for A, B other sequences in the
OEIS.  Call a "core" of the OEIS is a collection C of sequences from
which all other OEIS sequences can be defined as A union B, A
intersect B, or A setminus B for A for A and B in C.  I imagine a
minimum core of the OEIS would contain a minority of the sequences.