Identify integer sequences by terms, search the OEIS, read formulas, programs, b-files, cross-refs.
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List sequences related to an OEIS entry. direction outgoing returns the A-numbers named in the entry's cross-reference (Cf.) lines, with any parenthetical note beside each; direction incoming returns entries that mention this A-number anywhere. Each row carries the related sequence's name and first terms. 10 rows per page.
OEIS A-number, e.g. "A000045"; oeis_identify_sequence and oeis_search_sequences return them. Also accepts "a000045", "A45", "45", and an oeis.org sequence URL; all normalize to the zero-padded form. Legacy M/N book numbers (e.g. "M1459") are not A-numbers: find them with oeis_search_sequences.
Row offset: 0, 10, … 100 (at most 110 rows are reachable per entry and direction). Pass nextStart from the previous page.
outgoing (default): the A-numbers this entry cross-references. incoming: the entries that mention this A-number.
List sequences related to an OEIS entry. direction outgoing returns the A-numbers named in the entry's cross-reference (Cf.) lines, with any parenthetical note beside each; direction incoming returns entries that mention this A-number anywhere. Each row carries the related sequence's name and first terms. 10 rows per page.
| Argument | Type | Description |
|---|---|---|
| start | integer | Row offset: 0, 10, … 100 (at most 110 rows are reachable per entry and direction). Pass nextStart from the previous page. |
| aNumber* | string | OEIS A-number, e.g. "A000045"; oeis_identify_sequence and oeis_search_sequences return them. Also accepts "a000045", "A45", "45", and an oeis.org sequence URL; all normalize to the zero-padded form. Legacy M/N book numbers (e.g. "M1459") are not A-numbers: find them with oeis_search_sequences. |
| direction | string | outgoing (default): the A-numbers this entry cross-references. incoming: the entries that mention this A-number. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"aNumber"
],
"properties": {
"start": {
"type": "integer",
"default": 0,
"maximum": 100,
"minimum": 0,
"multipleOf": 10,
"description": "Row offset: 0, 10, … 100 (at most 110 rows are reachable per entry and direction). Pass nextStart from the previous page."
},
"aNumber": {
"type": "string",
"description": "OEIS A-number, e.g. \"A000045\"; oeis_identify_sequence and oeis_search_sequences return them. Also accepts \"a000045\", \"A45\", \"45\", and an oeis.org sequence URL; all normalize to the zero-padded form. Legacy M/N book numbers (e.g. \"M1459\") are not A-numbers: find them with oeis_search_sequences."
},
"direction": {
"enum": [
"outgoing",
"incoming"
],
"type": "string",
"default": "outgoing",
"description": "outgoing (default): the A-numbers this entry cross-references. incoming: the entries that mention this A-number."
}
},
"additionalProperties": false
}Fetch one OEIS entry by A-number. Returns the name, data-line terms, offset, keywords, author, dates, and the sections: comments, formulas (recurrences and generating functions), examples, programs (Maple, Mathematica, PARI, Python, …), references, links, cross-references, and extensions. When the sections together exceed 24,000 characters of serialized JSON, the core fields come back with a section outline instead; call again with sections to pick what to read. A selection past 100,000 bytes comes back in parts cut between items: pass nextFromItem as fromItem, with the same sections, for the next part.
| Argument | Type | Description |
|---|---|---|
| aNumber* | string | OEIS A-number, e.g. "A000045"; oeis_identify_sequence and oeis_search_sequences return them. Also accepts "a000045", "A45", "45", and an oeis.org sequence URL; all normalize to the zero-padded form. Legacy M/N book numbers (e.g. "M1459") are not A-numbers: find them with oeis_search_sequences. |
| fromItem | object | Where to resume a cut selection: the previous response's nextFromItem, passed unchanged with the same sections. The selected sections before fromItem.section are left out. Omit to start at the beginning. |
| sections | array | Sections to return with the core fields, e.g. ["formulas", "programs"]. A selection past the 100,000-byte response budget is cut between items; fromItem continues it. Omit (or pass []) for the full entry, or the core fields plus an outline when the entry is large. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"aNumber"
],
"properties": {
"aNumber": {
"type": "string",
"description": "OEIS A-number, e.g. \"A000045\"; oeis_identify_sequence and oeis_search_sequences return them. Also accepts \"a000045\", \"A45\", \"45\", and an oeis.org sequence URL; all normalize to the zero-padded form. Legacy M/N book numbers (e.g. \"M1459\") are not A-numbers: find them with oeis_search_sequences."
},
"fromItem": {
"type": "object",
"required": [
"section",
"index"
],
"properties": {
"index": {
"type": "integer",
"maximum": 9007199254740991,
"minimum": 0,
"description": "0-based position of the item within its section."
},
"section": {
"enum": [
"comments",
"formulas",
"examples",
"programs",
"references",
"links",
"crossReferences",
"extensions"
],
"type": "string",
"description": "Section name."
}
},
"description": "Where to resume a cut selection: the previous response's nextFromItem, passed unchanged with the same sections. The selected sections before fromItem.section are left out. Omit to start at the beginning."
},
"sections": {
"type": "array",
"items": {
"enum": [
"comments",
"formulas",
"examples",
"programs",
"references",
"links",
"crossReferences",
"extensions"
],
"type": "string"
},
"description": "Sections to return with the core fields, e.g. [\"formulas\", \"programs\"]. A selection past the 100,000-byte response budget is cut between items; fromItem continues it. Omit (or pass []) for the full entry, or the core fields plus an outline when the entry is large."
}
},
"additionalProperties": false
}List terms a(n) of a sequence with their indices n. Reads the entry's b-file when it has one — often thousands of terms beyond the data line — and otherwise the data line itself. Values are exact decimal strings of any size. A slice stops at limit terms (at most 1000 per call), at about 100,000 bytes, or at the end of one 1 MiB part of a larger b-file, whichever comes first; nextFromIndex continues it.
| Argument | Type | Description |
|---|---|---|
| limit | integer | Maximum number of terms to return (default 100). One call returns at most 1000, so a larger limit is served as 1000. A slice stops sooner at about 100,000 bytes of large terms or at the end of one 1 MiB part of a larger b-file; continue with nextFromIndex. |
| aNumber* | string | OEIS A-number, e.g. "A000045"; oeis_identify_sequence and oeis_search_sequences return them. Also accepts "a000045", "A45", "45", and an oeis.org sequence URL; all normalize to the zero-padded form. Legacy M/N book numbers (e.g. "M1459") are not A-numbers: find them with oeis_search_sequences. |
| fromIndex | integer | First index n to return; defaults to the first available index. Pass nextFromIndex from the previous call to continue. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"aNumber"
],
"properties": {
"limit": {
"type": "integer",
"default": 100,
"maximum": 9007199254740991,
"minimum": 1,
"description": "Maximum number of terms to return (default 100). One call returns at most 1000, so a larger limit is served as 1000. A slice stops sooner at about 100,000 bytes of large terms or at the end of one 1 MiB part of a larger b-file; continue with nextFromIndex."
},
"aNumber": {
"type": "string",
"description": "OEIS A-number, e.g. \"A000045\"; oeis_identify_sequence and oeis_search_sequences return them. Also accepts \"a000045\", \"A45\", \"45\", and an oeis.org sequence URL; all normalize to the zero-padded form. Legacy M/N book numbers (e.g. \"M1459\") are not A-numbers: find them with oeis_search_sequences."
},
"fromIndex": {
"type": "integer",
"maximum": 9007199254740991,
"minimum": -9007199254740991,
"description": "First index n to return; defaults to the first available index. Pass nextFromIndex from the previous call to continue."
}
},
"additionalProperties": false
}Identify integer sequences that contain a run of consecutive terms, e.g. "1, 2, 5, 14, 42". Returns up to 10 matches per page in OEIS relevance order, each with the index n at which the supplied run begins. For the best hit rate supply about 6 terms and leave off the first one or two, since sources disagree on where a sequence starts. OEIS matches only the first terms of each entry (its data line, at most about 270 characters), not its b-file, so a run from far into a sequence is not found. Takes up to 60 terms, each an integer of at most 200 digits or the wildcard _ for one unknown term.
| Argument | Type | Description |
|---|---|---|
| start | integer | Result offset: 0, 10, … 100 (OEIS shows at most 110 results per query). Pass nextStart from the previous page. |
| terms* | string | Up to 60 consecutive terms separated by commas or spaces, e.g. "1, 2, 5, 14, 42" (a bracketed list or a trailing ... is accepted). Each term is an integer of at most 200 digits, or _ for a single unknown term. |
| matchSigns | boolean | false (default) matches ignoring signs, so a sign-convention difference does not hide the sequence; true requires the signs to match. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"terms"
],
"properties": {
"start": {
"type": "integer",
"default": 0,
"maximum": 100,
"minimum": 0,
"multipleOf": 10,
"description": "Result offset: 0, 10, … 100 (OEIS shows at most 110 results per query). Pass nextStart from the previous page."
},
"terms": {
"type": "string",
"description": "Up to 60 consecutive terms separated by commas or spaces, e.g. \"1, 2, 5, 14, 42\" (a bracketed list or a trailing ... is accepted). Each term is an integer of at most 200 digits, or _ for a single unknown term."
},
"matchSigns": {
"type": "boolean",
"default": false,
"description": "false (default) matches ignoring signs, so a sign-convention difference does not hide the sequence; true requires the signs to match."
}
},
"additionalProperties": false
}Look up OEIS vocabulary used by the other tools: keyword flags (nonn, core, tabl, cons, …), search syntax (prefixes, operators, wildcards, sort orders, paging window), and identifier conventions (A-numbers, legacy M/N numbers, offsets, b-files).
| Argument | Type | Description |
|---|---|---|
| topic* | string | keywords: keyword flags such as nonn, core, tabl. search_syntax: prefixes, operators, wildcards, sort orders, and paging. identifiers: A-numbers, legacy M/N numbers, offsets, and b-files. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"topic"
],
"properties": {
"topic": {
"enum": [
"keywords",
"search_syntax",
"identifiers"
],
"type": "string",
"description": "keywords: keyword flags such as nonn, core, tabl. search_syntax: prefixes, operators, wildcards, sort orders, and paging. identifiers: A-numbers, legacy M/N numbers, offsets, and b-files."
}
},
"additionalProperties": false
}Search the OEIS using its query syntax: plain words, "quoted phrases", comma-separated terms, prefixes (keyword:, author:, name:, comment:, formula:, program:, xref:, id:), | for OR, and a leading - to exclude. Returns up to 10 summaries per page. For identifying a sequence from its terms, oeis_identify_sequence is the direct route.
| Argument | Type | Description |
|---|---|---|
| sort | string | Result order: relevance (default), number (ascending A-number), created (newest entry first), or modified (most recently edited first). |
| query* | string | OEIS query, sent as written. Examples: keyword:core fibonacci; author:Sloane; "Catalan numbers" (a quoted phrase); 1,2,5,14,42 (separate terms with commas: with spaces alone, a negative term after the first starts a new run and fewer than three numbers are not joined). oeis_list_reference topic search_syntax lists the prefixes and operators. |
| start | integer | Result offset: 0, 10, … 100 (OEIS shows at most 110 results per query). Pass nextStart from the previous page. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"query"
],
"properties": {
"sort": {
"enum": [
"relevance",
"number",
"created",
"modified"
],
"type": "string",
"default": "relevance",
"description": "Result order: relevance (default), number (ascending A-number), created (newest entry first), or modified (most recently edited first)."
},
"query": {
"type": "string",
"maxLength": 1000,
"minLength": 1,
"description": "OEIS query, sent as written. Examples: keyword:core fibonacci; author:Sloane; \"Catalan numbers\" (a quoted phrase); 1,2,5,14,42 (separate terms with commas: with spaces alone, a negative term after the first starts a new run and fewer than three numbers are not joined). oeis_list_reference topic search_syntax lists the prefixes and operators."
},
"start": {
"type": "integer",
"default": 0,
"maximum": 100,
"minimum": 0,
"multipleOf": 10,
"description": "Result offset: 0, 10, … 100 (OEIS shows at most 110 results per query). Pass nextStart from the previous page."
}
},
"additionalProperties": false
}