  Collatz conjecture is generalized to $3n+3^k$ ($k\in N$). Operating as usual,
every sequence seems to reach $3^k$ and end up in the loop $3^k, 4.3^k,
2.3^k,3^k$. The usual $3n+1$ conjecture is recovered for $k=0$. For $k>0$, we
noticed the existence of a sequence of period 3, namely, $3^{k-1}, 2.3^k, 3^k$,
alongside the cycle $4.3^k, 2.3^k,3^k$ encountered in the $3n+1 (k=0)$
sequence. A term formula of the $3n+3^k$ conjecture has been derived, and hence
the total stopping time.
