10-digit clock sequence

[Jacques Tramu]

Re: Seeking an endorsement for arXiv.orgnice work and nice show, Eric .

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http://www.echolalie.com/gbnums
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  ----- Original Message ----- 
  From: Eric Angelini 
  To: seqfan at ext.jussieu.fr 
  Sent: Saturday, May 03, 2008 5:50 PM
  Subject: 10-digit clock sequence


  Hello SeqFans,

  Remember this 10-digit clock ?

  >                0
  >         9      *      1
  >          *           *
  >
  >     8 *                 * 2
  >                .
  >
  >     7 *                 * 3
  >
  >          *           *
  >         6      *      4
  >                5

                          +
                           734

  This clock is used as a compass to draw the landing point of any integer somewhere on the plane, like in this example: take the integer 734 and put it at the center of the clock (coordinates 0,0); now go one step-unit in direction 7, then one step-unit in direction 3, then one step-unit in direction 4: you'll land on the cross, above (under the 4-digit). This spot is the landing point of 734 -- but also of 347, 473, and (infinitely) many more, as you'll notice quickly.

  I have asked Jean-Marc Falcoz, a friend of mine, to compute the sequence of integers hitting a free point on the plane (so 21 is not in the sequence because 21 lands on an already existing point -- the one drawn by 12); the sequence starts like this (soon to appear in the OEIS, Neil accepting):

  S=0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,28,29,30,33,34,35,36,37,39,40,44,45,46,47,48,55,56,57,58,59,60,66,67,68,69,70,77,78,79,80,88,89,90,99,100,101,102,...

  Jean-Marc has drawn the resulting figure, step by step (sorry for the twice printed link, this is a bug in my PC which I have not fixed -- yet):

  http://membres.lycos.fr/aideciste/prim100opt.gif

  The same compass is used to draw the path of Pi, e, SQR2, etc. here (page in french): 

  http://www.cetteadressecomportecinquantesignes.com/Falcoz4.htm

  Best,

  E.
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