# [seqfan] Prime and composite walks concatenated

Eric Angelini Eric.Angelini at kntv.be
Mon Apr 26 16:28:39 CEST 2010

```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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