Also not true when n=0 for those who like the initial term to be $P_0$. I've edited the answer to make it technically correct.
– Martin HansenMar 08 '19 at 17:11
@MartinHansen A $0$-digit number makes no sense to my opinion. But the restriction to $n>1$ is a useful edit.
– PeterMar 08 '19 at 17:42