Changelog
Changes to the results and writing on this site, newest first. 2 of them are corrections, listed here rather than changed silently.
- CorrectionThe summary said this check is linked from Terence Tao's database of Erdős problems. The database links the OEIS tree-count sequence, added by my pull request; the summary now says that. Checking an Erdős conjecture on every tree, three sizes further than before
- UpdateSaid exactly how far the second program agreed (up to six cells), relabeled the exact-fraction rebuild as an internal check, and added the third count (the fixed count, already in the OEIS since late August) to the text of this page. Counting the shapes you can build from the Josehedron
- UpdateThe check box no longer says the count match shows each tree was produced once; it shows none were lost or added overall. Checking an Erdős conjecture on every tree, three sizes further than before
- UpdateCorrected the explanation of the open question: a finite table can prove that a game repeats (a theorem of Guy and Smith), but not that it never does. Extending an expert's tables for unsolved take-away games in a way he could check himself
- UpdateSaid exactly what the tables' maintainer reran: the largest game over his old range, two other games over their full new ranges, and a fourth game matching later. Extending the tables for a set of unsolved take-away games, checked and built on by the expert who keeps them
- UpdateCorrected the explanation of why the open question is open: a finite table can prove that a game repeats (a theorem of Guy and Smith), but it cannot prove that one never does. Added the game's rules and what counts as a rare value. Extending the table for one unsolved take-away game to four times its published length
- UpdateAdded that the solid's shape had already appeared, without a name, in Moritz Schmitt's survey of such solids. Counting the shapes you can build from the Josehedron
- CorrectionThe Erdős tree check's title and claim now name the independent-set sequence (the counts of ways to pick dots with no line between them), the one the problem is about. Checking an Erdős conjecture on every tree, three sizes further than before
- UpdateA398957, the count of shapes that may only be slid into place (the fixed count), published in the OEIS, completing the family. Counting the shapes you can build from the Josehedron
How recently the numbers were checked
The site uses 108 numbers, each stored once with its source. A number that can change carries the date it was last checked; none has gone more than 120 days without a check.