A004258
loading terms
The Groundtruth Seam · a catalogue measured
How Many Terms Are Enough?
Move a prefix-length control through a frozen OEIS catalogue audit, after reproducing a published duplicate with the same literal stored-term instrument.
The OEIS FAQ says that about six terms are usually enough for a lookup, and advises starting with the second because beginnings disagree. That is practical guidance, not a census. Before counting the whole catalogue, this page makes its instrument answer a question whose answer OEIS has already published.
The duplicate must agree
A004258 is published as “Duplicate of A029837.” and marked dead. The two frozen term vectors below pass through the same equality test used by the census.
Anchor comparatorcomparing frozen records
A029837
loading terms
terms compared
computing
literal stored integers
terms agreeing
computing
term for term
mismatches
computing
before any new count
Now let the catalogue thin out
Each bar is a prefix length. Move the slider or click a bar. The browser sums unordered pairs from the frozen group-cardinality ledger, using exact integer arithmetic.
Literal prefix censusloading the ledger
selected prefixother prefix lengthsvertical scale: log base 10 of pair count
unordered pairs sharing k terms
computing
all outcomes retained
eligible A-numbers
computing
enough displayed terms
collision groups
computing
largest group computing
later mismatch witnessed
computing
exact duplicate link
computing
equal visible vectors
computing
shorter record ends
computing
These four buckets are disjoint. A pair carrying an exact parsed duplicate link is removed from its natural later-mismatch, visible-tie, or censoring bucket and placed in the duplicate bucket.
The new measurement is the conditioned table, not a probability of mathematical identity.
We could not find this published as of 2026-08-01, having searched the OEIS FAQ and Hints, the OEIS draft page “Minimum number of terms to uniquely identify a sequence,” OEIS Download and GitHub materials, arXiv, and exact web queries for OEIS prefix collisions and sequence-identification term counts.
“That curve is made of conventions”
The sophisticated dismissal: leading zeros, disputed starting positions, duplicate records, short vectors, and huge constant families manufacture the curve. The controls below rerun the full ledger under those objections. The hazard plot holds later visibility fixed so disappearing short records cannot masquerade as identification.
Convention laboratoryliteral, all records, constants retained
Vacuous setting: every one-term prefix is constant, so suppressing constant prefixes at k = 1 removes every eligible record by construction. The k = 2 bar is the nearest genuine comparison.
Does one more visible term split the pair?
conditional next-term split rate
computing
computing numerator and denominator
Pairs visible through the required next term
Pairs that split at that next stored term
The catalogue is curated and dependent, so none of these ratios is a birthday probability. The drop-opening-term mode changes the literal vector start; it does not apply OEIS subsequence matching, ranking, offsets, signs, or b-files.
The check
The browser recomputes every displayed count from a computing-byte distilled ledger. The offline verifier independently recomputes the census results from the frozen official bulk files, then executes this page engine and tests nine deliberate corruptions.
| snapshot | OEIS bulk files fetched 2026-08-01 10:51:09 UTC |
|---|---|
| sequence rows | computing in stripped.gz |
| name rows | computing in names.gz |
| anchor | computing |
| baseline convention | k = 6, literal stored terms, all records, constants retained |
| baseline total | computing unordered pairs |
| integer rule | exact strings and JavaScript BigInt, no numeric term conversion |
| duplicate rule | unique unordered links from exact names matching Duplicate of A######. |
- “Stored term” means position in
stripped.gz, not a(0), a(1), or any offset-aware alignment. Offsets are absent from that bulk file. - A later mismatch requires a differing integer at a position stored by both records. Equal vectors of equal visible length remain exact visible ties. When one equal prefix ends sooner, the pair is right-censored.
- The exact name parser finds computing duplicate-name records. Qualified phrases such as “Essentially a duplicate” and “Incorrect duplicate” are not silently treated as clean links.
- The bulk-file headers give the same instant; all 364 extra name rows are allocated-for placeholders with no sequence rows. The denominator always comes from
stripped.gz. - Only displayed bulk terms are measured. B-files may be longer. OEIS search uses consecutive subsequences and relevance ranking, neither of which this literal-prefix census imitates.
- Free choices are the snapshot epoch, prefix start, k from 1 to 20, record-name exclusion, constant-prefix exclusion, outcome scope, and minimum later visibility of k + 1 or k + 5 terms.
node research/oeis-collision/verify-oeis-collision.mjs
The published record beside the audit
The OEIS FAQ supplies the about-six-terms guidance and the advice to omit one or two opening terms. The closest prior treatment we found is the unfinished OEIS Wiki draft “Minimum number of terms to uniquely identify a sequence”. It gives examples and the rule of thumb, but no catalogue-wide conditioned table.
The term and name records come from the official OEIS downloads. They are reused under CC BY-SA 4.0, with attribution to The Online Encyclopedia of Integer Sequences. The anchor records are A004258 and A029837.
A prefix is not an identity
This page does not estimate the probability that a newly computed mathematical object is identical to an OEIS entry. That would require a prior over how researchers generate sequences, semantic comparison of definitions, offset-aware alignment, b-file depth, and the behavior of the actual OEIS search ranker.
Nor does a visible tie prove two records define the same infinite object. The honest next step is to freeze full metadata and offsets at the same epoch, then test alignment and definitions without turning absence of a stored mismatch into evidence of identity.
Corrections
Corrected 2026-09-29: the page called the bulk snapshots asynchronous and said they disagreed; their headers give the same instant, and the 364 extra name rows are allocated-for placeholders with no sequence rows. Found by the source-first pilot, 2026-09-28. Corrected 2026-09-29: the draft citation used a URL that redirects to login; the plain title URL, now cited, serves the same revision, 1641482, as of 2026-09-29. Found by the source-first pilot, 2026-09-28. Corrected 2026-09-29: the relates note said the pile sequence was extended by one term; that page gives two, a(5) = 819 and a(6) = 2555. Found by the source-first pilot, 2026-09-28. Corrected 2026-09-29: the page said every listed corruption had to turn the check red; the pair-coefficient control also changed a group multiplicity, and the witness and date controls did not run the real comparisons. Those three controls now test the actual comparisons on true and corrupted inputs. It also said the verifier rebuilds the ledger and checks every group size; it recomputes the census results and checks the number of collision groups and the largest group. Found by the source-first pilot, 2026-09-28. See the assay.