Solve recurrence: T(n) = T(n/ logn) + O(1)

Question

Can you help me solve this recurrence formula and find out the Big-oh?
T(n) = T(n/logn) + O(1)
I've tried recursion tree method but it didn't help!

Answer 1

It looks like $k$ iterations of $n/\ln(n)$ gives about $n/\ln^k(n)$ so this stops when $n/\ln^k(n)=1$ or $k = \ln(n)/\ln(\ln(n))$.