Q: Can some rigorous sense of "meaningfulness" be introduced to characterize relations? A little goofy, but this question occurred to me in the context of the following example. While answering a strictly-programming question at https://stackoverflow.com/questions/44482735/#44491340 I generated the following list of six numbers that are the only integers between 1 and 10million whose representations as numerals in both base 3 and base 4 are "palindromic"...
        10(base10) = 101(3) = 22(4)
       130(base10) = 11211(3) = 2002(4)
     11950(base10) = 121101121(3) = 2322232(4)
    175850(base10) = 22221012222(3) = 222323222(4)
    749470(base10) = 1102002002011(3) = 2312332132(4)
   1181729(base10) = 2020001000202(3) = 10200200201(4)

Okay, so that maybe seems a slight curiosity, but also seems pretty meaningless, i.e., having (as far as I can tell) no number-theoretic significance whatsoever. But, what, it occurred to me, does "meaningless" rigorously mean? We can introduce the perfectly well-defined characteristic function (aka relation) $f:\mathbb{N,N^2}\to\{0,1\}$ such that $f(i;j,k)=1$ iff $i\in\mathbb{N}$ is "palindromic" in both bases $j,k$ (and $=0$ if not). So that's a perfectly legitimate $f$, but also perfectly (or approaching perfectly) "meaningless".
But how can you characterize that more rigorously? For example, I can rigorously characterize a sequence of numbers as "random" by their Kolmogorov complexity (or by various other rigorous measures). On the other hand, we can pretty safely characterize this "palindromic function" as meaningless by "inspection". And that intuitively seems pretty much true, i.e., it's meaningless.  But there doesn't seem to exist any rigorous approach to such a characterization. Can you conjure one up?
