[seqfan] Re: Golay-Rudin-Shapiro sequences

[allouche at math.jussieu.fr]

Dear all

The link between paperfolding and Golay-Shapiro's sequence
can be found in essence in a paper by Mendes France and
Tenenbaum, see the remark on lines 7--8, p. 212 of the paper
accessible at
http://www.numdam.org/item?id=BSMF_1981__109__207_0

best
jpa

Neil Sloane <njasloane at gmail.com> a écrit :

> 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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>
>
>
> --
> 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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