[seqfan] Masses and antimasses -- equilibrium / desequilibrium

Eric Angelini Eric.Angelini at kntv.be
Thu Oct 8 15:05:03 CEST 2009

```Hello SeqFans,
first row is n
second row is a mass or an 'antimass' ('antimasses' are underlined
with this symbol: « ^ »)

0123456789
021.......
^
We have above an equilibrium, because of the eguality of
(arm) x (mass/antimass):

Mass    Antimass
2 x 1 = 1 x 2
^
Now that we have an equilibrium, we convert the antimass in a
regular mass, producing thus a desequilibrium:

0123456789
021.......

What would be the smallest possible mass 'x' and antimass 'y'
producing a new equilibrium?                               ^

0123456789
021xy.....
^
We must resolve the simple equation (3×x)+(2×1)+(1×2)= 4×y
or [3x+4=4y] which gives the values x=0 and y=1.         ^
^                                 ^
We have thus the new equilibrium:

0123456789
02101.....
^
We brake the equilibrium and iterate:

0123456789
02101xy...
^
Equation: (5×x)+(4x1)+(3x0)+(2x1)+(1x2)= 6×y
or [5x+8=6y] which gives the values x=2 et y=3

We have thus the new des/equilibrium:

0123456789
0210123xy...
^
Equation --> 7x+36=8y --> x=4 and y=8 --> des/equilibrium:

0123456789
021012348xy...
^
Equation --> 9x+128=10y --> x=8 and y=20 --> des/equilibrium:

n = 0 1 2 3 4 5 6 7 8 9 10 11 12
S = 0,2,1,0,1,2,3,4,8,8,20, x, y,
^
Equation --> 11x+400=12y --> x=4 and y=37 --> des/equilibrium:

n = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
S = 0,2,1,0,1,2,3,4,8,8,20, 4,37, x, y,
^

Equation --> 13x+888=14y --> x=14 and y=901 --> des/equilibrium:

n = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
S = 0,2,1,0,1,2,3,4,8,8,20, 4,37,14,901,x, y,
^
etc.

Could one check and compute a few more terms of this strange seq.?
Best,
É.

```