[seqfan] Re: Golay-Rudin-Shapiro sequences
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!
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
> but I worry it's not reading very clearly yet :-)
> Even the white bits were black.
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Neil J. A. Sloane, President, OEIS Foundation
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Email: njasloane at gmail.com
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