Doubly logarithmic tree

In computer science, a doubly logarithmic tree is a tree where each internal node of height 1, the tree layer above the leaves, has two children, and each internal node of height $$h > 1$$ has $$2^{2^{h-2}}$$ children. Each child of the root contains $$\sqrt{n} $$ leaves. The number of children at a node from each leaf to root is 0,2,2,4,16, 256, 65536, ... A similar tree called a k-merger is used in Prokop et al.'s cache oblivious Funnelsort to merge elements.