Comment on What is your interesting fact or knowledge that is completely useless that you wish to share?

HexesofVexes@lemmy.world ⁨1⁩ ⁨week⁩ ago

• stoicmaverick@lemmy.world ⁨1⁩ ⁨week⁩ ago

  do it now…

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  • HexesofVexes@lemmy.world ⁨1⁩ ⁨week⁩ ago

    Let $\mu(x)=0$ if $\exists y<x\mu(y)=0$ or $x$ is the 20 millionth prime. $\mu(x)=\mu(x+1)+1$ otherwise. The elements of the sequence only become defined once the 20 millionth prime is found; till then they’ve yet to be constructed.

    Bonus: The sequence $\nu$ is defined as follows.

    Let $\nu(x)=0$ if $\exists y\leq x\mu(y)$ is perfect. $\nu(x)=\nu(x+1)+1$ otherwise.

    We’re not sure if this is a sequence, even though it is algorithmically definable. Its existence relies on the existence of an odd perfect number.

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