When I was 18 I was at a mathematical gathering at which John Conway was also present, and we somehow got talking. He took a brown A4 envelope and on the back wrote that sequence of fractions and told me what to do with them. An unforgettable experience.
Suppose we replace the number x by the number xf, where f is the first fraction in the list below such that xf is also an integer. If you do this repeatedly from x = 2, then the powers of 2 that appear are 2^2, 2^3, 2^5, ..., 2^p for all primes p https://en.wikipedia.org/wiki/FRACTRAN pic.twitter.com/TKKNgECRc2
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How astonishing that must have seemed!
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I'm now fighting the urge to write a brainfuck to fractran compiler
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Why fight the urge?
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Why does it work, the way it does? It's so cool and mind-bending at the same time.
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Fractran is Turing-complete. Here is an NP-complete problem with input to Fractran: Can you flip some of the the fractions and get 1 by multiplaying all fractions? Nice puzzle.
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