  The Collatz problem with $3x+k$ is revisited. Positive and negative limit
cycles are given up to k=9997 starting with $x_0=-2\cdot10^7...+2\cdot10^7$. A
simple relation between the probability distribution for the Syracuse iterates
for various k (not divisible by 2 and 3) is obtained. From this it follows that
the oscillation considered by Tao 2019 ( arXiv:1909.03562v2 ) does not depend
on k. Thus this piece of the proof of his theorem 1.3 "Almost all Collatz
orbits attain almost bounded values" holds for all k not divisible by 2 and 3.
