Integer Sequence Identifier

$0.10 USDC per call · Research integrity · POST /api/v1/identify-sequence · Id sequence-identifier

Identifies an integer sequence from terms (a JSON array or pasted text), an OEIS A-number, a safe-parsed formula or recurrence, or a description, and leads with a verdict, confidence, A-number, formula, next terms and a next step. Searches the OEIS directly, then superseeker-style (differences, partial sums, gcd, ratios, binomial, Euler, leading terms, plus a search without the last two terms to flag disagreeing terms) under an 8-search budget, aligns offsets, and marks which terms agree or disagree. Fits linear recurrences and polynomials exactly over the rationals and reports one only when it predicts held-out terms. Candidates are ranked in code; a model is used only for a description input (one fast call, OEIS confirms what it proposes) and for the optional explain sentence (one more call, quote verified against OEIS text). Output carries the CC BY-SA 4.0 OEIS attribution.

What you get

Turns a list of numbers into its OEIS A-number, formula and next terms in one call, or a verified recurrence or polynomial when OEIS has none.

Call it

Send the JSON body below to https://agents.writerslogic.com/api/v1/identify-sequence. An unpaid request answers 402 with the price and how to pay; a request that fails with a 5xx status is not charged.

curl -i -X POST https://agents.writerslogic.com/api/v1/identify-sequence \
  -H 'content-type: application/json' \
  -d '{"terms":[1,1,2,5,14,42,132,429,1430,4862]}'

Input

Field	Type	Required	Description
`terms`	array<one of>; max 60 items	no	Integer terms, 4 to 60, each at most 40 digits. Pass values beyond 2^53 as decimal strings.
`termsText`	string; length 4..4000	no	Alternative to terms: the terms pasted as text, separated by commas, spaces or semicolons (for example copied from a spreadsheet, a paper or an OEIS data line).
`aNumber`	string; length 1..120	no	Alternative to terms: an OEIS A-number (A000108) or oeis.org URL. The entry is fetched and its data searched for related sequences; returns its name, formulas and next terms.
`formula`	string; length 1..300	no	Alternative to terms: a closed form in n such as "binomial(2n,n)/(n+1)", or a recurrence such as "a(n) = a(n-1) + a(n-2)" (with initialTerms). Operators + - / % ^, functions binomial fact abs gcd min max floor mod. Evaluated by a safe parser, never eval; every term must be an integer.
`initialTerms`	array<one of>; max 20 items	no	Seed values a(start), a(start+1), ... for a recurrence formula.
`start`	integer; -100..1000	no	Index n of the first expanded term; default 0.
`count`	integer; 4..60	no	How many terms to expand from the formula; default 20.
`description`	string; length 3..500	no	Alternative to terms and formula: a plain-language description. A short description that names an entry (up to 4 content words, all in the entry name, e.g. Catalan numbers) is resolved by OEIS text search with no model; otherwise one fast model call proposes terms and keywords, which OEIS then confirms.
`explain`	boolean	no	Ask a model for a one-sentence explanation drawn only from the matched OEIS entry; its quote is verified in code, otherwise the entry name is returned. Default false.

Example request body

{
  "terms": [
    1,
    1,
    2,
    5,
    14,
    42,
    132,
    429,
    1430,
    4862
  ]
}

Result

The response is { "data": ..., "_provenance": ... }. data carries these fields; _provenance is a signed W3C Verifiable Credential with a C2PA-style manifest, checked free at POST /api/v1/verify-provenance.

Field	Type	Required	Description
`answer`	object	no	Headline: verdict (same as status), confidence 0-100, aNumber, name, url, formula and formulaSource (oeis or fitted), nextTerms (from a verified fit), alsoConsistentWith, a one-sentence summary and a concrete nextStep.
`status`	string; one of "IDENTIFIED", "IDENTIFIED_VIA_TRANSFORM", "PARTIAL_MATCH", "RECURRENCE_ONLY", "NO_MATCH"	no
`input`	object	no	kind, termsSource (caller, formula, model, oeis-entry or oeis-text-search), the terms analyzed, the expanded formula and any model keywords.
`candidates`	array<object>	no	Ranked OEIS candidates: aNumber, url, name, evidence, transform used (null = direct), alignment (OEIS index of the first compared term), matched/mismatched terms, unverified terms beyond the entry's data, exact, formulas, references.
`explanation`	one of	no	One line from OEIS text only: the entry name, or a model sentence whose quote was verified (source oeis-name or model).
`recurrence`	one of	no	Constant-coefficient linear recurrence solved exactly over the rationals from the first 2*order terms; reported only when it reproduces every later term (heldOutTerms >= 2).
`polynomial`	one of	no	Polynomial in n from vanishing finite differences, reported only with held-out terms predicted exactly.
`search`	object	no	OEIS searches made (budget 8, sequential and rate limited), steps skipped or not applicable, and failures.
`llmCalls`	integer	no
`llmFailures`	integer	no
`decidedBy`	object	no	Where the terms, ranking and explanation came from.
`attribution`	object	no	OEIS source and the CC BY-SA 4.0 notice.
`notes`	array<string>	no

Pay and connect

Available through: x402 (USDC on Base), MCP, RapidAPI, Apify.

Machine-readable

This agent as JSON (schemas, example, OpenAPI operation)
Free signed sample response
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