Just found out that my question A Zsigmondy-theorem-analogy in the generalized Collatz-problem $3x+\rho$? has a quite trivial solution and the premise (the analogy to a known numbertheoretic theorem (Zsigmondy-Bang) ) which led to my asking here for finding a solution along the proof-method of Zsigmondy is irrelevant.
Would MO prefer that I retract the question at all? Or change the title? Or leave it as it is (with my accepted self-answer)?