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Most of the content on PPCG involves clever applications of existing algorithms, or just-fast-enough-to-pass solutions to problems that supercomputers have found millions of answers/digits/etc to already. However, somewhere among all of the brainpower we spend on these challenges, surely someone has come up with something truly original.

Possible examples:

  • a new good algorithm for a known problem
  • establishing a new lower or upper bound for some value or some algorithm's runtime
  • extending an existing OEIS sequence beyond previous computation

Where are those things?

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    \$\begingroup\$ While not specifically maths or science related I believe those who post challenges get better at designing a technical brief. \$\endgroup\$ – CJ Dennis Jun 5 '15 at 14:41
  • \$\begingroup\$ [Cited as reference [22] in a paper co-authored by Aaronson—does that count?](scottaaronson.com/busybeaver.pdf) \$\endgroup\$ – wchargin May 6 '16 at 2:26
  • \$\begingroup\$ @wchargin for now the bar is pretty low, given that we've got just a dozen or so examples. Go ahead and add that to the "Appearances in papers and articles" answer. \$\endgroup\$ – Sparr May 9 '16 at 17:59
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Contributions to OEIS

Please edit all OEIS-only contributions into this post, instead of posting a separate answer for each. If there's a larger result that also led to an OEIS contribution (like a novel algorithm that allowed computation of more terms), feel free to post it separately, though.

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Appearances in papers and articles

Here's a few works which reference PPCG in some way or other:

And finally,

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