How I found and fixed a number that was wrong in the OEIS for over a decade

The OEIS (the Online Encyclopedia of Integer Sequences) is the public database of number sequences that mathematicians use and cite. For 14 years, one of its entries listed a number with a digit missing. Its thirteenth term read 1,150,036. The right value is 11,500,336. Put them side by side and the short one is the long one with a 3 left out.

What the entry counts#

The entry is A202182. It counts N-free posets of each size. A poset is a set of items where some pairs are ranked against each other and others are not. Picture each item linked to the items directly above it. A poset is N-free if no four items have direct links that form the letter N (two items at the bottom, two at the top, linked in a zigzag) with no other ranking among those four. Posets that are the same apart from the names of their items count once.

Each new term takes a lot of computing, so once a value is in the table, people usually copy it rather than recompute it.

Why it stayed wrong so long#

The wrong value was there from the entry's first version in 2011. In 2021 someone editing the entry filled in the term just before it, the twelfth, which had been missing. Adding a new term gives no reason to recompute the ones already listed, so the thirteenth stayed as it was.

How it was spotted#

In July 2026 I had eight Claude agents scouting for new projects, each in a different area. The one covering discrete math and the OEIS compared A202182 with its two companion entries, which split the same posets in two: those that come in one connected piece (A202180) and those that do not (A349367). For any size, those two counts should add up to the total in A202182. For size 13 they are 8,840,306 and 2,660,030, which add up to 11,500,336, not the listed 1,150,036.

How it was confirmed#

A sum like that is a strong hint, but I did not want to send a correction based on it alone, so I had the value worked out four times, by two separate routes, before submitting anything. These were not four independent checks: the first two both start from the listed counts in A202180, and the last two are full counts of the same kind, run in two separate sessions. The two routes, one built from the listed entries and one counting every poset directly, do not depend on each other. The first was the sum itself, recomputed from the live entries: it fails at size 13 and holds at every other size. The second built the total from the connected counts alone, using a standard formula that assembles posets from their connected pieces; it gave 11,500,336 and matched every other listed term. The third and fourth were full from-scratch enumerations of every N-free poset with 13 items, run in two separate sessions. Both gave 11,500,336, split into 8,840,306 connected and 2,660,030 not.

The correction#

I submitted the correction together with freshly computed values for the terms around it, and the OEIS editors approved it in July 2026. The entry now carries the correction with credit. In August 2026 I added the next new term to the same entry, the fifteenth, 435,034,695. It came from a rewritten enumerator that first reproduced the family's published tables through size 14, and the number of disconnected posets it implies matches the separately published value in A349367 exactly.

For readers in software:how the software was built, and which parts you could reuse

What found this bug was a cross-table invariant: two derived tables must add up to a third. A single table can be wrong for years with nothing inside it to contradict it. If related tables in your own data must satisfy an identity like this, assert it and check it whenever any of them changes, because a value that is expensive to recompute will mostly be copied, not checked.

@misc{orden2026oeistypohunt,
  author       = {Tyler Satchel Orden},
  title        = {How I found and fixed a number that was wrong in the OEIS for over a decade},
  year         = {2026},
  howpublished = {Cyborg Mathematics},
  url    = {https://cyborgmathematics.com/writing/oeis-typo-hunt}
}