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The 3x+3k generalised Collatz mapping
Consider the mapping Tk: ℤ → ℤ
where k ≥ 0:
Tk(x)={x/2 if x is even,(3x+3k)/2 if xis odd.
In an email dated 2nd February 2001, Willem Maat observed that the sequence of iterates x,Tk(x),T2k(x),… eventually becomes 3km for some odd integer m and
subsequently the iterates become 3km,3kT0(m), 3kT20(m),…, where T0 is the Collatx 3x+1 mapping.
Conseqently one expects to reach one of the cycles defined by 0,3k,−3k,−5×3k,−17×3k.
This was also recently communicated to me on 31st October 2024 by David Barina.
There is a BC version available.
Last modified 7th November 2024
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