Energy efficiency is one of the most important issues of Wireless sensor networks (WSN) due to limited battery capacity. In sink-centric WSN (i.e., sensing data is collected by the sink node), this issue is particularly challenging due to the 'funnel effect' which means high energy consumption of the nodes near the sink. While clustering can be used to achieve scalability of WSN, previous works on energy optimal design of the cluster structure have limitations in the scalability. In this paper, we propose a scheme to build an energy optimal cluster structure for a sink-centric WSN. The most important finding of this paper is that energy optimality depends only the size of first three clusters from the sink node. Based on this finding, we design a very scalable clustering algorithm for optimal network lifetime. The algorithm is highly scalable since its time complexity is independent of the network size. We verify the correctness of the algorithm by comparing with the optimal results that are found by exhaustive search. Numerical evaluations are performed by modeling the off-the-shelf radio links such as IEEE 802.15.4 and IEEE 802.11.