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May 10, 2023 at 23:49 comment added Peter Taylor If there is a fixpoint $f(m)=m$ then $f(a_m) = a_{m+1} = a_{f(m)+1} = a_m$ and the sequence has a non-constant prefix followed by a constant tail.
May 10, 2023 at 23:00 comment added Wojowu $f$ defined by $f(0)=1,f(2k-1)=2k,f(2k)=2k-1$ for all $k>0$ seems to work. I have no idea about classification.
May 10, 2023 at 22:40 history edited TheSimpliFire CC BY-SA 4.0
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May 10, 2023 at 22:27 comment added Wojowu I'm assuming you also want such a sequence $a_n$ to exist - otherwise the implication is vacuously true.
May 10, 2023 at 22:08 history asked TheSimpliFire CC BY-SA 4.0