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 ${\displaystyle h>1}$ has ${\displaystyle 2^{2^{h-2}}}$ children. Each child of the root contains ${\displaystyle {\sqrt {n}}}$ leaves.^[1] The number of children at a node from each leaf to root is 0,2,2,4,16, 256, 65536, ... (sequence A001146 in the OEIS)

A similar tree called a k-merger is used in Prokop et al.'s cache oblivious Funnelsort to merge elements.^[2]