Hi !!! I have no idea how to do this question help please !!

Sylvester caught n mice which he arranged in a circle and numbered them 1,2,...,n in clockwise order. Starting with mouse number 1, Sylvester went around the circle in clockwise order, skipping over one mouse and eating the next one. He went round and round by the same rule, until only one mouse was left. This lucky mouse was then set free. Denote f(n) as the number assigned to the lucky mouse initially. Now f(1)=1, f(2)=1, f(3)=3, f(4)=1, and f(5)=3

a) Express f(2n) and f(2n+1) in terms of f(n)

b) given that f(530)=37, determine f(2121).