[seqfan] Re: morphism in A284940 compared with A080580

Kimberling, Clark ck6 at evansville.edu
Tue Apr 25 14:15:10 CEST 2017

A quick check found these:

A284683 related to A081692 and A081693
A285820 to A189664
A284948 to A171946 and A171947

The following are ready to be submitted (next few days I hope):
A285383 related to A171946 and A171947
A285430 to A026363 and A026364
A285431 to A026367 and A026364
A285671 to A045671 and A045672.

At least some of those position sequences seem to be of the type at A080580.

Best regards,
Clark Kimberling

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil Sloane
Sent: Tuesday, April 25, 2017 5:13 AM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Cc: seqfans <seqfan at seqfan.eu>
Subject: [seqfan] Re: morphism in A284940 compared with A080580

In other words, RJM is saying that it appears that

 "the positions of 0's in the fixed point of the morphism 0 -> 01, 1 -> 1101"
are given by
"a(1)=1; for n>1, a(n)=a(n-1)+2 if n is already in the sequence,
a(n)=a(n-1)+4 otherwise".

That is a pretty interesting conjecture (A284940 =? A080580)!  It would be worth checking it for a few million terms, or more.

Clark Kimberling (if you are on this list), I know you have recently been studying many similar "Positions of 0's in fixed point of ..."
sequences.  Have you observed any other apparent coincidences of this type?
Best regards

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

On Tue, Apr 25, 2017 at 3:28 AM, Richard J. Mathar <mathar at mpia-hd.mpg.de> wrote:
> The first 1000 terms (at least) of A284940 equal the first
> 1000 terms of A080580. Can this be demonstrated for all general values?
> Richard
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