Terence Tao merged my second pull request, adding OEIS links to seven more Erdős problems

On September 18, 2026, the mathematician Terence Tao merged a second pull request of mine into his GitHub database of Erdős problems. It links seven more Erdős problems to sequences that were already in the OEIS (the Online Encyclopedia of Integer Sequences). A pull request is a proposed change on GitHub, and merging it accepts the change.

The site erdosproblems.com shows the database's links on each problem's public page, so these seven links now appear on seven more problem pages there. With the tree problem's link, merged on August 6, that makes two pull requests of mine accepted into a database Tao maintains. Both merges came after my check of every tree at three sizes past the old limit, whose last run finished on August 4.

The sequences in these links are the work of other OEIS contributors; none of them is mine. What I added is the connection between each problem and its sequence.

How the seven were found#

The database marks a problem "possible" when a matching sequence may already be in the OEIS but nobody has linked one. On September 4, Claude agents working under my direction read the statement of every problem marked that way with no sequence linked yet, picked the ones most likely to be in the OEIS already (those that define a concrete whole-number count or list with a short definition), and searched the OEIS for each. The agents judged each match; I asked them to open the pull request under my name once the matches were confirmed.

A match had to agree with the problem in its definition. Agreeing in the first few numbers was not enough, because two different counts can agree for a while and then part. The database's own guide warns about this. Each of the 19 searched problems that did not match was recorded with the reason. For two of the matches the agents also recomputed values themselves and compared them with the OEIS: the list for problem 1140, recomputed for every number below 20000, and the count for problem 308 for every N up to 24.

Before the pull request was opened on September 5, a last check against the live database found that one of the eight, problem 694, had been given its links by someone else since the agents' copy was taken. That one was dropped. Every one of the seven sequences was fetched again from the live OEIS and matched.

What was proposed#

Each link was a one-line edit, in the same format as the tree link. For five problems the "possible" mark stayed, because other sequences could still be linked later. For two problems (942 and 943) the linked sequences cover what the problem defines, so the mark was removed, as the database's guide says to do in that case. One link (problem 634) was a looser fit than the others, and the pull request said so and offered to drop it. The description disclosed that the screening, the OEIS lookups and the small recomputations were done with the help of Claude (Anthropic), and said that no new sequence was being sent to the OEIS.

The merge#

Tao merged all seven edits on September 18, Pacific time, the looser fit for problem 634 included. He left no comments or review on the pull request. As with the first pull request, a merge accepts the links into the database. It does not say anything about the problems themselves, several of which are still open.

For specialists: the seven links

Problem	What it asks about	Linked OEIS entries	"possible" kept
308	For each N, the smallest whole number that is not a sum of distinct unit fractions 1/d with every d from 1 to N	A101877, the inverse function (for each whole number n, the least largest denominator needed to reach n)	yes
634	The numbers n for which some triangle can be cut into n congruent triangles	A005792, the case where the pieces are also similar to the whole; its comments discuss the congruent-only case	yes
939	Sums of coprime r-powerful numbers	A297867 (3-powerful numbers that are sums of two coprime 3-powerful numbers) and A036966 (3-full numbers)	yes
942	h(n), the number of powerful numbers from n² up to but not including (n+1)²	A119241, which counts those strictly between n² and (n+1)², so h(n) is A119241(n) plus one, for n² itself; and A119242	no
943	The number of ways to write n as a sum of two powerful numbers	A085252 (unordered pairs; the problem counts ordered pairs), A085253, A085255	no
1140	The n with n − 2x² prime for every x with 2x² below n (x = 0 included, so n itself is prime)	A240842, the same condition for x of at least 1; its prime terms are exactly the list on the problem page	yes
1161	The number of elements of order k in the symmetric group on n letters	A057731, exactly this triangle	yes

The pull request is teorth/erdosproblems #399↗. Its description gives each definition, the indexing and ordering conventions where they differ from the problem's, and the repository's validation script's result on the edited file: the same pre-existing schema errors as the untouched base and nothing new.

This page tells the story as of the merge on September 18, 2026. When I last checked, on October 29, 2026, all seven links were still in the database, and the pages on erdosproblems.com for problems 942 and 1161 showed their new links under the heading "From the external database".

@misc{orden2026erdosdatabasesevenmorelinks,
  author       = {Tyler Satchel Orden},
  title        = {Terence Tao merged my second pull request, adding OEIS links to seven more Erdős problems},
  year         = {2026},
  howpublished = {Cyborg Mathematics},
  url    = {https://cyborgmathematics.com/writing/erdos-database-seven-more-links}
}