Oeis MCP Server

@cyanheads/oeis-mcp-server Identify integer sequences by terms, search the OEIS, read formulas, programs, b-files, cross-refs via MCP. STDIO or Streamable HTTP. 6 Tools • 1 Resource

Public Hosted Server: https://oeis.caseyjhand.com/mcp

Overview

Integer sequences from the On-Line Encyclopedia of Integer Sequences (OEIS). Identify a sequence from a few observed terms, search with OEIS's own query syntax, read an entry's formulas and programs, page through extended terms from its b-file, and walk its cross-references. Every result links to its oeis.org page. No API key required.

Tools

Resources

The same record is available through oeis_get_sequence for clients that only call tools.

Capability reference

oeis_identify_sequence tool

• terms: up to 60 consecutive terms separated by commas or spaces (a bracketed list or a trailing ... is accepted), each an integer of at most 200 digits or _ for one unknown term; matchSigns (default false) ignores signs unless set
• Up to 10 candidates per page, start 0–100 in steps of 10; each row carries the oeis_search_sequences row fields plus matchStartIndex, the n where the run begins in that entry's data line (absent when the run isn't there)
• No match and "too many results" both return an empty page; the notice says which and how to retry (drop leading terms, divide out a common factor, or add terms). OEIS matches a run only within each entry's data line (at most about 270 characters), never its b-file, and a zero-hit notice says so when every nonzero term has 10 or more digits, five or more terms of 4 or more digits lie within 10% of each other, or the run passes 270 characters

oeis_search_sequences tool

• query (1–1,000 characters) is sent as written: words, "quoted phrases", term lists, prefixes such as keyword:, author:, name:, formula:, xref:, and id:, | for OR, and a leading - to exclude
• sort: relevance (default), number, created, or modified; 10 per page, start 0–100 in steps of 10
• Rows carry name, terms, offset / firstIndex, keywords, author, legacyIds, modified (the last edit, ISO 8601 with offset), and url, in oeis_get_sequence's formats; author and legacyIds are absent where OEIS has none
• Reports totalCount and effectiveQuery, the query as OEIS parsed it. A query OEIS parses as one run of terms (effectiveQuery reads seq: or signed: and the terms, as for bare numbers separated by commas) is matched within each entry's data line, as in oeis_identify_sequence, and its zero-hit notice names that limit under the same conditions
• With spaces alone between numbers, OEIS starts a new run at a negative term after the first and does not join fewer than three numbers; when effectiveQuery shows that split, the notice says so and gives the terms joined by commas to search as one run

oeis_get_sequence tool

• Returns name, terms, offset / firstIndex, keywords, author, legacyIds, referenceCount, revision, created / modified, url, and bFileUrl, plus eight sections: comments, formulas, examples, programs, references, links, crossReferences, extensions
• When the sections exceed 24,000 characters of serialized JSON, kind: "outline" returns the core fields and a sized sections list; pass sections (e.g. ["formulas", "programs"]) to get the chosen ones
• A selection past 100,000 bytes comes back in parts cut between whole items; pass each part's nextFromItem as fromItem, with the same sections, for the next. A fromItem naming a section not in sections fails as from_item_not_selected
• An unknown A-number fails as sequence_not_found; withdrawn (dead), reserved, and recycled entries come back with a notice

oeis_get_terms tool

• fromIndex (default: the first available index) and limit (default 100; one call returns at most 1,000 terms, so a larger limit is served as 1,000); a slice also stops at about 100,000 bytes or at the end of a 1 MiB part of the b-file, and nextFromIndex continues it
• source: "bfile" reads the entry's b-file in 1 MiB parts, so a fromIndex past the first 1 MiB costs one or two more paced requests; bFileCut: true means the file goes on past lastAvailableIndex. source: "data" means the entry has no b-file and the terms are its data line
• Terms come back as { n, value }, value an exact decimal string; an unknown A-number fails as sequence_not_found
• A b-file line that is not blank, a # comment, or an n a(n) pair is skipped, and the notice says how many; a b-file that holds no pair at all fails as upstream_unparseable and is not cached

oeis_get_cross_refs tool

• direction: "outgoing" (default) lists the A-numbers named in the entry's cross-reference lines, with the note written beside each and the lines verbatim; "incoming" lists the entries that mention the A-number
• 10 rows per page, start 0–100 in steps of 10; every row carries url, and resolved rows add the name, terms, offset, keywords, author, legacy IDs, and last edit (modified)
• If the name lookup for an outgoing page is rate-limited, unavailable, or times out, rows come back resolved: false with a retry notice instead of failing; sequence_not_found applies to outgoing only

oeis_list_reference tool

• topic: keywords (flags such as nonn, core, tabl, cons), search_syntax (prefixes, operators, wildcards, sort orders, paging), or identifiers (A-numbers, legacy M/N numbers, offsets, b-files)
• Returns entries (name, description) and notes from static tables

oeis://sequence/{aNumber} resource

• The full entry as application/json: the record oeis_get_sequence returns with kind: "full", never outlined
• aNumber takes the same forms as the tools (oeis://sequence/A108 reads A000108); an unknown A-number fails as sequence_not_found

Features

Built on @cyanheads/mcp-ts-core: stdio and Streamable HTTP transports, pluggable auth (none / jwt / oauth), swappable storage (in-memory, filesystem, Supabase, Cloudflare KV/R2/D1), structured logging with optional OpenTelemetry tracing.

OEIS-specific:

• One paced, cached oeis.org client (see Pacing and caching); searches tell "no results" apart from "too many results" and report the match total
• Forgiving A-numbers: A000045, a000045, A45, 45, and an oeis.org sequence URL all resolve in every tool; a legacy M/N book number is pointed to oeis_search_sequences
• Exact terms: every term and b-file value is a decimal string, so values past 2^53 keep every digit
• Pasted term runs are normalized: brackets, a trailing ..., the Unicode minus sign, and mixed comma and space separators

Agent-friendly output:

• Paging context on every page (truncated, shown, cap, plus totalCount and effectiveQuery where OEIS reports them) and a notice that says how to narrow or continue
• Typed failures with recovery hints: sequence_not_found, from_item_not_selected, upstream_unparseable, pacer_shed, and upstream_rate_limited, the rate-limit errors carrying retryAfter when one is known
• Discriminated outputs (kind, source, per-row resolved), so callers branch on data, not string parsing
• Every record and row carries its https://oeis.org/A###### URL; contributor-written text renders as code spans and code fences, so a markdown client shows formulas and names exactly as written, and only http and https link URLs are kept

Pacing and caching

oeis.org asks automated clients to wait 10 seconds between requests. The server sends one upstream request at a time and starts each at least 10 seconds after the last, across every tool. Results are cached in memory, so a repeated lookup returns at once and costs oeis.org nothing: records for 24 hours, or until a search result shows a later edit (then revalidated with a conditional request), search pages for 1 hour, and b-file parts for 7 days. An entry's cached "no b-file" answer is dropped as soon as a fetched record lists a b-file.

A call with nothing cached waits its turn in the queue. When the wait would pass OEIS_QUEUE_MAX_WAIT_MS (default 30,000 ms), the call fails with pacer_shed and a retryAfter instead of hanging. If oeis.org answers 429, the server holds every queued call back before trying again, and reports upstream_rate_limited once its retries are spent. The pace is per server process.

Known limitations

• Anonymous paging is capped upstream at 110 results per query (start ≤ 100); A000045's 6,161 incoming references, for example, are reachable only through their first 110.
• A query OEIS judges too broad returns no rows ("Too many results"), which is common f