base-$n$ numbers (including leading zeros), where $n$ is number of buttons. Second, while majority of enumerated codes is invalid, checking RPN syntax is very fast, almost negligible compared to `itoa` itself, let alone to computation of complex exponential and logarithmic functions. Procedure has two loops: outer for code length $K$, inner enumerating $n^K$ codes of length $K$. Inner loop is trivial to parallelize using OpenMP directives without effort, scaling linearly with number of physical cores. Moreover, hyper-threading is utilized as well, although scaling is only at quarter of core count. Therefore, prospects for high-utilization of modern high-end multi-core CPU’s [@epyc] are looking good. Digits are associated with RPN calculator buttons. For simplest case they are ternary base digits `012`, which were assigned to three RPN calculator buttons as: 0 $\to$ E ($e$), 1 $\to$ LOG ($\log_x{y}$), 2 $\to$ POW ($x^y$). Detailed example of the algorithm for is presented in Appendix A of Supplemental Material.

Combinatorial growth of the enumeration is characterized, in addition to Kolmogorov complexity (RPN code length) $K$, by a total number of possible codes tested so far $k_1$. It grows with $K$ as: $$k_1 = \sum_{K'=1}^{K} n^{K'} = \frac{n^K-1}{n-1} n.$$ Total number of syntactically correct codes $k_2$ 