Key points are not available for this paper at this time.
Collatz conjecture is generalized to 3n+3ᵏ (k N). Operating as usual, every sequence seems to reach 3ᵏ and end up in the loop 3ᵏ, 4. 3ᵏ, 2. 3ᵏ, 3ᵏ. The usual 3n+1 conjecture is recovered for k=0. For k>0, we noticed the existence of a sequence of period 3, namely, 3^k-1, 2. 3ᵏ, 3ᵏ, alongside the cycle 4. 3ᵏ, 2. 3ᵏ, 3ᵏ encountered in the 3n+1 (k=0) sequence. A term formula of the 3n+3ᵏ conjecture has been derived, and hence the total stopping time.
Naouel Boulkaboul (Wed,) studied this question.