[seqfan] Re: Aperiodic palindromes

Joerg Arndt arndt at jjj.de
Thu Nov 25 10:45:51 CET 2010

* Charles Greathouse <charles.greathouse at case.edu> [Nov 25. 2010 09:00]:
> There are several sequences in the OEIS dealing with "aperiodic
> palindromes".  First of all, I think it would be good if these
> sequences either defined the term or clearly linked to a sequence with
> its definition.

It would be good to have a local copy of
  M. R. Nester (1999).
  Mathematical investigations of some plant interaction designs.
  PhD Thesis. University of Queensland, Brisbane, Australia.

>  Second, some are marked with keyword:base but in my
> understanding (possibly wrong) they are not base-dependent.

The keyword base shouldn't be there as far as I see.

>  Would
> someone with more knowledge of this care to comment?

I assume the "aperiodic" refers to circular shifts,
e.g. A056458 Number of primitive (aperiodic) palindromes \
             using a maximum of two different symbols

1: 0 and 1
2: none (palindromes are 11 and 00 but both are periodic)
3: 101 and 010 (111 and 000 are periodic)
4: 1001 and 0110

Obviously all terms are divisible by 2.
Similalry, all terms of A056459 are divisible by 3.

> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
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