[seqfan] 0's and 1's in Wilson's cubefree A282317

Neil Sloane njasloane at gmail.com
Thu May 4 20:20:04 CEST 2017

Maximilian, A week ago I started to create "Positions of 0's in A282317"
and "Positions of 1's in A282317".  But I didn't do it
because at that time the entries had not been confirmed.

Now that you have confirmed them, and you made a similar suggestion,
could you go ahead and create those two entries?  And you mentioned
the run-lengths, which would be two more.  It would certainly
be appropriate for you to create them.  If you tell me the A-numbers I'll
approve them.  Thanks!

By the way, I like your program for A282317 - although I only read the
"text" version
you sent to the SeqFans list.

Just to make sure I'm reading it correctly:

What  increment(W) does is to take the input word W and looks for the
last 0 in it, say
W = ABCDE011111
and changes it to
W = ABCDE1, right?

Then you take the present cubefree string S, and
start with W = S, and repeatedly "increment" W
until you reach a W such that S' = SW is cubefree, and SW is the new S.

If no increment was needed, you keep W the same and repeat.
If it was necessary to increment W, the new W is SW, and again you repeat.

- Have I understood the algorithm correctly?

This is nice because it generates the sequence in ever-increasing
chunks, as follows (I think):

(better check!)

The lengths of these chunks are
1,2,3,5,6,8,15,30,43,... (done by hand, probably has errors)
which would be a new sequence - can you get more terms? (And feel free
to submit it).  If we understood that sequence we might learn
something about A282317.

More information about the SeqFan mailing list