The Syracuse conjecture for U(0)={2,4,6,8,...,256} -monodimensional display- [*La conjecture de Syracuse pour U(0)={2,4,6,8,...,256} -visualisation monodimensionnelle-*].

- The Syracuse sequence is defined as follows:

U = N (an integer number [

*un nombre entier*]) > 0 0

if U is even [*si U est pair*] : n n

U n U = ---- n+1 2

else [*sinon*] :

U = 3*U + 1 n+1 n **The Syracuse conjecture**states that sooner or later the {[[4,] 2,] 1} sequence will appear whatever the starting number N (and then repeats itself obviously*ad vitam aeternam*). For example with U(0)=7:U(0) = 7 U(1) = 22 U(2) = 11 U(3) = 34 U(4) = 17 U(5) = 52 U(6) = 26 U(7) = 13 U(8) = 40 U(9) = 20 U(10) = 10 U(11) = 5 U(12) = 16 U(13) = 8 U(14) =

**4**U(15) =**2**U(16) =**1**

Here are 256 different sequences starting from U(0)=1 to U(0)=256.

- The horizontal and vertical axes represent the integer numbers {2, 4, 6, 8,...}. Each vertical line (with abscissa equals to N) displays the sequence U(n) starting at U(0)=N and the color of each of its points {N,U(n)} is a function of 'N'.

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(CMAP28 WWW site: this page was created on 09/13/2017 and last updated on 05/06/2020 10:58:05 -CEST-)

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