By definition, this is {s: A072207(s) < 2*A072207(s-1)}. [R. J. Mathar, Oct 30 2010]

EXAMPLE

The set size in A072207 doubles with the first 5 transformations, 1->2->4->8->16->32. a(1)=6 because the 6th application grows the set only 32->52 (to less than 64).