Golomb sequence ($G(n)$)

The nondecreasing sequence of positive integers beginning with $G(1)=1$ in which the integer $n$ occurs exactly $G(n)$ times. Its first terms are $1,2,2,3,3,4,4,4,5,5,5,\dots$. The prefix sum ${\sum }_{j=1}^{k}G(j)$ gives the last position occupied by $k$.