a_a =: 1 + +
  a_b =: [ % +.

  py (a_b ` a_a @. has_gcd) y

I know it is math and all that, but when we commit something like this at day job, it doesn’t give you applause. Can the idea of the article be expressed in more readable/obvious form? Or is that an alphabet that you should learn first before solving that?

It’s a problem without solutions, when implementing from a mathematical definition.

Either you write it so it is “easy” to understand or you write it so it is easy to compare with the source equation.

Both have pros and cons.

Any two functions when glued together as a piecewise function can have a discontinuity, that's true, but that’s not what this is... this is a sequence with a recursive term. Sort of like the fibonacci sequence where a term is defined by the one preceding it, so you have to, conceptually, computer all the way down to the base case. It just so happens that the rule in this article for some reason becomes very well ordered past a certain step when you plot the values, at least to our human brains.

The numberphile video to which the article links is a good watch!