A048823 a(n) = value of n defined as follows: start with n and reach 2 by repeatedly either dividing by d where d <= the square root or by subtracting 1. The division steps are free, but subtracting 1 costs 1 point. The "value" of n is the smallest cost to reach 2.

1, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 1, 2, 3, 1, 2, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 1, 1, 1, 2, 1, 2, 0, 1, 2, 3, 0, 1, 2, 1, 0, 1, 1, 2, 1, 2, 1, 2, 0, 1, 1, 1, 2, 2, 1, 2, 0, 1, 1, 2, 0, 1, 2, 3, 2, 3, 1, 1, 2, 2, 3, 2, 0, 1, 1, 1, 1, 2, 1, 2, 1