The Syracuse conjecture for U(0)={2,3,5,7,...,719} -monodimensional display- [*La conjecture de Syracuse pour U(0)={2,3,5,7,...,719} -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 axis represents the prime numbers P={2, 3, 5, 7, 11,...},
when the vertical axis represents the integer numbers {1, 2, 3, 4, 5,...}.
Each vertical line (with abscissa equals to P) displays the sequence U(n) starting at U(0)=P
and the luminance of each of its points {P,U(n)} is proportional to 'n'. For example with P=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**

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(CMAP28 WWW site: this page was created on 01/15/2013 and last updated on 02/28/2022 11:11:33 -CET-)

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