Count And Say

Count And Say

Given a string of digits that is guaranteed to contain only digit characters from 0123456789, read that string “out loud” by saying how many times each digit occurs consecutively in the current bunch of digits, and then return the string of digits that you just said out loud.

example

As silly and straightforward as this count-and-say sequence problem might initially seem, it required the genius of a mathematician of no lesser caliber than the late great John Conway himself not only to notice the tremendous complexity ready to burst out from just below the surface when this operation is repeatedly iterated to produce an infinite sequence of such digit strings, but also capture that whole mess into a symbolic polynomial equation, as the man himself explains in this video.

You can also check out the related construct of the infinitely long and yet perfectly self-describing Kolakoski sequence where only the lengths of each consecutive block of digits is written into the result string, not the actual digits.

example

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