The Kruskal–Katona function, Conway sequence, Takagi curve, and Pascal adic

We study interrelations between the Kruskal–Katona function, Conway sequence, Takagi curve, and Pascal adic. Using the results of the current paper and, in particular, the convergence of the sequence $2a(n)-n$, where $a(n)$ is the Conway sequence, to the family of generalized Takagi curves, we prove a similar result for the Kruskal–Katona function. Moreover, a recursive method of computing the values of the Kruskal–Katona function is suggested.