[seqfan] Re: Ian Hutchinson's EckXOR sequence

[Ian Hutchinson]

On the topic of subsidiary sequences, I have one in mind that might be
useful to explore. I altered my Python code to record the y value used in
the XOR operation for each term, and compiled those into a list of their
own. This may be useful in understanding the original sequence, as it could
function as a new angle to view behaviors from. So far I've noticed that
each term tends to be no more than one more than the last, and it seems to
have a cool looking graph of its own (https://imgur.com/a/zm7TxQd).
The formal definition of this sequence would probably look something like
one of these two:
a(n) = the number of m < n such that A340488(m) = A340488(n)
a(n) = XOR(A340488(n), A340488(n-1))
I don't know if I'll have the time to flesh out an entry for this alongside
all of my college classes this week, so anyone who's interested in this is
more than welcome to make an entry for it.

Also, I just wanted to give a brief thanks to Neil, the OEIS editors, and
all the other community members who have been so helpful and open over the
past few days. The fact that I pitched it as a brand new OEIS user a little
over two days ago and it's now an approved sequence with
multiple subsidiary seqs is amazing to me.

Best,
Ian

On Sun, Jan 10, 2021 at 5:17 PM Neil Sloane <njasloane at gmail.com> wrote:

> Dear SeqFans, Ian Hutchinson mentioned a variant of Van Eck's sequence here
> the other day. It is now A340488, and Remy Sigrist and I have been studying
> it.  There are three subsidiary seqs A340494, -495, -496. It looks rather
> more understandable than the original Van Eck sequence.
>
> There is even a conjectured formula for the positions of the record high
> points.
> And the graph suggests that there just might perhaps possibly be a
> recurrence for the sequence itself. Look at the way those blocks of terms
> stack up.
>
> I'm calling it the EckXOR sequence  (short for "variant of Van Eck sequence
> based on the XOR operation")
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
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