What is best formular that define Collatz conjecture formular and collatz sequence formular ?

Jerrycurl12

6 years ago

LetN/⟨2⟩
N/⟨2⟩
be the equivalence classes of positive integers having the same odd factors, i.e. it has the equivalence class3​⋅​⟨​2​⟩​=​{​3​,​6​,​12​,​24​,​…​}
3⋅⟨2⟩={3,6,12,24,…}
as an element.
Then you have
f:N/⟨2⟩→N/⟨2⟩
f:N/⟨2⟩→N/⟨2⟩
f(x)=3x+
2
ν 2
(x)
f(x)=3x+2ν2(x)
where2
ν 2
(x)

2ν2(x)
is the highest power of 2
2
that dividesx
x
.
Then the Collatz conjecture states that f facts transitively, or equivalently that its orbit converges to
⟨2⟩
⟨2⟩
for all inputs.