# [seqfan] Re: binary expansion 1+0*

Charles Greathouse charles.greathouse at case.edu
Mon Mar 22 20:23:05 CET 2010

```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.

Similarly, I was wondering recently about the 'only finitely
differing' equivalence relation: A equiv B when A(n) *= B(n+k) for
some k and all n > N, where a *= b is true if a = b or a and b are
both undefined and false otherwise.  I suspect that ,fini, sequences
are the largest equivalent component in the OEIS, probably followed by
a few with trailing 0s or other constants.  What other components are
large?

Unfortunately the metadata in the OEIS is not strong enough to answer
either of these questions at the moment.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Mar 22, 2010 at 3:01 PM, Graeme McRae <g_m at mcraefamily.com> wrote:
> Is there any need for a new sequence that could be defined as
> {A023758} - {A000079} ?
>
> --Graeme McRae,
> Palmdale, CA,
> Sent from my iPhone
>
> On Mar 22, 2010, at 11:51 AM, Joerg Arndt <arndt at jjj.de> wrote:
>
>> I erred, I wanted to exclude the powers of 2.
>> The pattern is 11+0* (and the initial 1 has
>> to be omitted in my seq).
>>
>> Thanks for correcting!
>>
>
>
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```