If we have the following $p$-adic number:
$$2+3p+5p^2+2p^3+3p^4+5p^5+2p^6+3p^7+5p^8+.....$$ and I am trying to find what rational number this p-adic number represents. I have no idea as to how to go about doing this. The only thing that I can notice is that maybe we need to split this up into cases where $p<5$ and $p\geq 5$ because otherwise this is some non-standard representation.
Cheers