[seqfan] Re: Golay-Rudin-Shapiro sequences

Neil Sloane njasloane at gmail.com
Tue Jun 12 17:12:56 CEST 2012


Kevin, If you didn't already do so, please add
some comments to the entries in the OEIS describing
the connections that you discovered
between the paper-folding
sequences and the GRS sequence!

Neil

On Mon, Jun 11, 2012 at 10:06 PM, Kevin Ryde <user42 at zip.com.au> wrote:

> njasloane at gmail.com (Neil Sloane) writes:
> >
> > I have been cleaning up a bunch of sequences related to the
> > Golay-Rudin-Shapiro (aka Rudin-Shapiro) sequence (or word).
> > The main sequence is A020985.
>
> I was tinkering recently with the connection of those to the alternate
> paper folding curve A106665.  I think that may be well-known, but my
> cribs as follows if it might inspire cross references.
>
>    A020985 -- Golay/Rudin/Shapiro sequence
>                 dX and dY, skipping every second value zero
>                 dSum, change in X+Y
>
>                 dX = GRS(N) if N even
>                      0      if N odd
>
>                 dY = 0      if N even
>                      GRS(N) if N odd
>
>                 dSum = dX + dY = GRS(N)
>
>    A020986 -- Golay/Rudin/Shapiro cumulative
>                 X coordinate undoubled
>
>    A020990 -- Golay/Rudin/Shapiro * (-1)^n, cumulative
>                 Y coordinate undoubled
>                 X-Y diff, starting from N=1
>
> I take the curve as first step along the X axis to X=1,Y=0 and then
> upwards to X=1,Y=1, etc.  By "undoubled" I mean the X coordinate doubles
> up as 0 then 1,1,2,2,etc and A020986 is every second such value.  Is the
> jargon "bisection"?  I suppose it's X=A020986(ceil(n/2)) or something
> like that, starting from n=0.
>
> Bit more notes I made under "dX,dY" code at
> http://search.cpan.org/perldoc?Math::PlanePath::AlternatePaper#dX%2CdY
> but I worry it's not reading very clearly yet :-)
>
>
>
>
> --
> Even the white bits were black.
>
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>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



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