WOLFRAM|DEMONSTRATIONS PROJECT

The 3n+1 Problem

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initial condition
50
⟶
25
⟶
76
⟶
38
⟶
19
⟶
58
⟶
29
⟶
88
⟶
44
⟶
22
⟶
11
⟶
34
⟶
17
⟶
52
⟶
26
⟶
13
⟶
40
⟶
20
⟶
10
⟶
5
⟶
16
⟶
8
⟶
4
⟶
2
⟶
1
Start with a number. Then at each step, if
n
is even, compute
n/2
, and if
n
is odd, compute
3n+1
. So far as anyone can tell, the resulting sequence always eventually reaches 1. But despite work since the 1930s, no proof is known.