[seqfan] Re: Prime and composite walks concatenated

Charles Greathouse charles.greathouse at case.edu
Mon Apr 26 16:43:53 CEST 2010

The first question is interesting to me: Does the sequence act like a
random walk?  Is it recurrent?  How does the behavior differ from the
same sequence over Cramér primes?

The second question is based on the behavior mod 360, which is
arbitrary and not so interesting to me.

Charles Greathouse
Case Western Reserve University

On Mon, Apr 26, 2010 at 10:28 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
> Hello SeqFans,
> I guess this is old hat -- but cannot find anything on the
> web or in my books:
> http://www.cetteadressecomportecinquantesignes.com/PrimeWalk.htm
> Best,
> É.
> ---------
> (...)
> Walking instructions:
> - Start at coordinates (0,0) facing North;
> - At each stage, you'll have to select the direction and the length of the walk (in steps);
> - The length of the walk is the same as the preceding one, plus one step;
> - The direction of the walk depends on its length: if the length is a prime number turn 90° to the left and walk; else turn 90° to the right and walk.
> A concatenation of the 16 first walks is shown on the sketch above.
> Question (1):
> - the 17th walk will pass through the starting point; are there other such walks? Could this be the start (0,1,17,...) of a new sequence for the OEIS?
> Question (2):
> - same question, but the direction of the walk is now given by its length "L": L degrees to the left (modulo 360) if L is prime, else L degrees (modulo 360) to the right.
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