Cyborg Mathematics

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Things that were computed and checked: new terms for sequences in the OEIS (the online database of integer sequences), computing records, counts, datasets and code. Each one shows when its numbers were last checked and how to reproduce them.

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Counting, games and networks3

An Erdős conjecture: in every tree, the number of ways to pick k dots with no two joined rises, then falls, as k grows. I checked every tree three sizes past the old limit; it held.
RecordPublishedChecking an Erdős conjecture on every tree, three sizes further than before· Aug 4, 2026
In July I pushed the published tables for a set of unsolved take-away games two to four times further. In four of the games, new heap sizes with rare values turned up.
RecordPublishedExtending the tables for a set of unsolved take-away games, checked and built on by the expert who keeps them· Jul 16, 2026· 3 versions
The largest table from the July take-away game work, taken four times past its published end after first reproducing the old table exactly. No new rare value appeared.
RecordPublishedExtending the table for one unsolved take-away game to four times its published length· Jul 5, 2026· 2 versions

Shapes that fill space1

Counts of the shapes you can build by gluing copies of the Josehedron face to face; the OEIS had none before. Mathias Bernhard named this space-filling solid this spring.
EnumerationPublishedCounting the shapes you can build from the Josehedron· verified Aug 15, 2026· 3 versions