 The Syracuse conjecture for U(0)={5,10,15,20,...,1310720} [La conjecture de Syracuse pour U(0)={5,10,15,20,...,1310720}].

• 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.

• Starting from the origin of the coordinates (at the center of the picture), one follows a square spiral-like path and numbers each integer point encountered (1, 2, 3,...):

```                    5----4----3
|         |    .
|         |    .
6    1----2    .
|              |
|              |
7----8----9----10
```

• At last, display the N-th point with the false color f(tst(N)) where:

```                    tst(N) = number of iterations of the Syracuse sequence starting with N before reaching the first {[[4,] 2,] 1} sequence (or Total Stopping Time).
```

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