some eta products

Sat May 3 16:26:29 CEST 2008

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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 so=
mewhere 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 dire=
ction 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 l=
anding 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 b=
ecause 21 lands on an already existing point -- the one drawn by 12); the s=
equence starts like this (soon to appear in the OEIS, Neil accepting):

S=3D0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,28,=
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 i=
n french):=20

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

Best,

E.

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<TITLE>Re: Seeking an endorsement for arXiv.org</TITLE>
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<P>Hello SeqFans,</P>
<P>Remember this 10-digit clock ?</P>
<P><FONT=20
size=3D2>>          &n=
bsp;    =20
0<BR>>        =20
9      *     =20
1<BR>>         =20
*          =20
*<BR>><BR>>     8=20
*            &n=
bsp;   =20
*=20
2<BR>>           =
    =20
.<BR>><BR>>     7=20
*            &n=
bsp;   =20
* 3<BR>><BR>>         =
=20
*          =20
*<BR>>        =20
6      *     =20
4<BR>>           =
    =20
5<BR><BR>           =
            =20
+<BR>           &nbs=
p;            =
=20
734<BR><BR></FONT>This clock is used as a compass to draw the landing =
point=20
of any integer somewhere on the plane, like in this example: take the integ=
er=20
734 and put it at the center of the clock (coordinates 0,0); now go one=20
step-unit in direction 7, then one step-unit in direction 3, then one=
=20
step-unit in direction 4: you'll land on the cross, above (under the=
=20
4-digit). This spot is the landing point of 734 -- but also of 347, 473, an=
d=20
(infinitely) many more, as you'll notice quickly.</P>
<P>I have asked Jean-Marc Falcoz, a friend of mine, to compute the sequence=
 of=20
integers hitting a free point on the plane (so 21 is not in the sequence be=
cause=20
21 lands on an already existing point -- the one drawn by 12); the sequence=
=20
starts like this (soon to appear in the OEIS, Neil accepting):</P>
<P>S=3D0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,=
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,...</P>
<P>Jean-Marc has drawn the resulting figure, step by step (sorry for the tw=
ice=20
printed link, this is a bug in my PC which I have not fixed -- yet):</P>
<P><A=20
href=3D"http://membres.lycos.fr/aideciste/prim100opt.gif">http://membres.ly=
cos.fr/aideciste/prim100opt.gif</A></P>
<P>The same compass is used to draw the path of Pi, e, SQR2, etc. here (pag=
e in=20
french): </P>
<P><A=20
href=3D"http://www.cetteadressecomportecinquantesignes.com/Falcoz4.htm">htt=
p://www.cetteadressecomportecinquantesignes.com/Falcoz4.htm</A></P>
<P>Best,</P>
<P>E.</P>

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