I want to order all numbers of the form $2^a3^b$. I need to find the average distance between a random consecutive pair.

For example, in case of a random consecutive pair $2^{n'}$ and $2^{n'+1}$, the distance is $2^{n'}$. Similarly, whats the distance between $2^{a_1}3^{b_1}$ and $2^{a_2}3^{b_2}$ such that there is no number of the form $2^{a}3^{b}$ between them.

Seems like an interesting problem.