OEIS.m Tutorial

A step-by-step walkthrough of OEIS.m, the Wolfram Language package for working with OEIS data. Every example on this page was run against the live OEIS JSON API with wolframscript — the printed output is real, not illustrative.

The runnable version of this tutorial lives at test/OEISTutorial.wl and doubles as an integration test: run it yourself with

wolframscript -file test/OEISTutorial.wl

The original package page, with its own usage examples, is on the OEIS wiki: User:Enrique Pérez Herrero/OEIS Package.

1. Load the package

Needs["OEIS`"]

Place OEIS.m on your $Path, or Get it directly:

Get["/path/to/OEIS.m"]

2. Validate an OEIS identifier

OEISValidateIDQ checks that a string has the canonical A + 6-digit shape used by OEIS.

OEISValidateIDQ["A000045"]
(* True *)

3. Build the sequence URL

OEISURL["A000045"]
(* "https://oeis.org/A000045" *)

Pass bFile -> True to get the b-file URL instead:

OEISURL["A000045", bFile -> True]
(* "https://oeis.org/b000045.txt" *)

4. Retrieve a sequence’s description

OEISImport["A000045", "Description"]
(* "Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1." *)

5. Retrieve the terms of a sequence

OEISImport[ID, "Data"] returns {n, a(n)} pairs, correctly offset to the sequence’s actual starting index (A000045 starts at n = 0, not n = 1):

OEISImport["A000045", "Data"][[1 ;; 5]]
(* {{0, 0}, {1, 1}, {2, 1}, {3, 2}, {4, 3}} *)

6. Inspect the available range

{OEISImport["A000045", "MinData"], OEISImport["A000045", "MaxData"]}
(* {0, 40} *)

7. Materialize a function from an OEIS sequence

OEISFunction defines A000045[n] in your session, preloaded with real data, and prints a short report:

OEISFunction["A000045"]

A000045(n): Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.
Link-1: https://oeis.org/A000045
Link-2: https://oeis.org/b000045.txt
Help Added: True
Loaded data from bFile: True
Loaded data from Sequence: False
Data available: Table of n, A000045(n) for n=0..40

A000045[10]
(* 55 *)

8. Export data and citations

OEISExport picks the output format from the file extension.

Wolfram help stub (.m):

OEISExport["A000045", "A000045.m"]

A000045::usage="A000045[n]: Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.";

BibTeX citation (.bib):

OEISExport["A000045", "A000045.bib"]

@MISC{oeisA000045,
AUTHOR={_N. J. A. Sloane_, 1964},
TITLE={The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
HOWPUBLISHED={\href{https://oeis.org/A000045}{A000045}},
MONTH={Apr},
YEAR={1991},
NOTE={Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.}
}

HTML citation (.html) and MediaWiki citation (.wiki) work the same way, and every OEISExport/OEISImport function accepts a list of IDs to batch-process several sequences at once.

9. Search OEIS

OEISSearch[text] searches by free text; OEISSearch[{n1,n2,...}] searches by a sequence of numbers. Both hit the same JSON endpoint OEISImport uses for ID lookup, just with a different query, and return up to 10 results (OEIS’s default page size) as a list of Entry Associations:

OEISSearch["prime gaps"][[1]]["ID"]
(* "A001223" *)

First[OEISSearch[{1, 1, 2, 3, 5, 8, 13}]]["ID"]
(* "A000045" *)

OEISRelated parses the IDs OEIS cross-references from an entry’s "xref" field (its “Cf. A000032, …” comments):

OEISRelated["A000045"][[1 ;; 5]]
(* {"A001622", "A039834", "A001519", "A001906", "A001690"} *)

OEISCitation[id, format] returns a citation string directly, without writing to a file – OEISExport’s .bib/.wiki output is built from it:

OEISCitation["A000045", "Wiki"]
(* "* {{oeis|A000045}}: Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1." *)

11. Structured data

OEISData[id] is a thin wrapper around OEISImport[id, "Entry"] – the whole entry as one Association, e.g. for Dataset[OEISData[id]]:

Keys[OEISData["A000045"]]
(* {"ID", "Description", "Author", "Date", "Offset", "Data", "Formula"} *)

12. The OEISSequence object

OEISSequence[id] is a lazy object wrapping one ID: nothing is fetched until a property is actually accessed.

seq = OEISSequence["A000045"];
seq["Values"][[1 ;; 10]]
(* {0, 1, 1, 2, 3, 5, 8, 13, 21, 34} *)

"Values" gives just the a(n) values, unlike "Data", which pairs them with n. "Keywords" gives OEIS’s own classification keywords:

seq["Keywords"]
(* {"nonn", "core", "nice", "easy", "hear", "changed"} *)

Other properties: "Data", "Plot", "Description", "Author", "Date", "Offset", "Formula", "References" (literature references – distinct from "Related"), "Related", "Graph", "Citation", "URL", "Entry".

OEISGraph[id] returns a Graph of id and the sequences OEISRelated finds for it, star-shaped around id – built from the one fetch OEISRelated already makes, no extra network calls per related sequence:

g = OEISGraph["A000045"];
{VertexCount[g], EdgeCount[g]}
(* {90, 89} *)

14. A random sequence

OEIS has no dedicated random-sequence endpoint, so OEISRandom[] picks a random A-number and retries on a miss (a withdrawn/merged/not-yet-assigned number), returning the Entry Association for whatever it lands on:

Keys[OEISRandom[]]
(* {"ID", "Description", "Author", "Date", "Offset", "Data", "Formula"} *)

If Import/URLFetch fail with curlLink_initialize was not loaded or OEIS::conopen even though the network is reachable, your Wolfram Engine’s bundled libcurllink.so is likely incompatible with the system’s OpenSSL (common on older Mathematica installs paired with a modern Linux distro). OEIS.m already works around this: OEISReadJSON automatically falls back to invoking the system’s curl (with LD_LIBRARY_PATH cleared, since Mathematica otherwise makes curl load its own bundled, older libcurl) whenever the built-in HTTP client fails.

Reference

Function Purpose
OEISValidateIDQ Validate an OEIS identifier’s shape
OEISImport Retrieve data, description, author, date, offset, etc.
OEISURL Build a sequence or b-file URL
OEISFunction Materialize ID[n] in your session
OEISExport Export to .m, .txt/.csv/.tsv, .bib, .html, .wiki, images
OEISbFile Write a b-file for a given ID up to a maximum index
OEISSearch Search by free text or by a sequence of numbers
OEISRelated IDs OEIS cross-references from an entry
OEISGraph A Graph of a sequence and its cross-references
OEISRandom The Entry Association for a randomly chosen sequence
OEISData The full entry as an Association, e.g. for Dataset
OEISCitation A "BibTeX"/"Wiki" citation string, without writing to a file
OEISSequence A lazy object wrapping one ID, with Plot/Values/Formula/… properties

See the Function Index for full signatures and options, the README for installation and project status, and CONTRIBUTING.md to send improvements.