# List of numbers

A list of numbers is a reference catalog of individual numbers or classes of numbers that are notable for a defined mathematical property, a fixed value, or a role in computation and history. Mathematicians organize such lists in several ways: by number type (integers, rationals, reals, complex numbers), by named classes with special properties (perfect numbers, weird numbers, [Fibonacci](https://www.edgepedia.org/fibonacci) numbers), and by mathematical constants whose values are fixed by unambiguous definitions.<sup>[1](https://mathworld.wolfram.com/Number.html)</sup>

| Key fact | Detail |
|---|---|
| Terminology | MathWorld uses "number" for quantities that are integers and reserves "constant" for nonintegral numbers with a fixed value.<sup>[1](https://mathworld.wolfram.com/Number.html)</sup> |
| Largest catalog of integer sequences | The On-Line Encyclopedia of Integer Sequences (OEIS) contained 400,158 sequences as of its most recent site update.<sup>[2](https://oeis.org/)</sup> |
| Origin of sequence tables | *A Handbook of Integer Sequences* (1973) was the first table of sequences of integers; before it, someone encountering 1, 1, 2, 5, 15, 52, 203, 877, 4140, ... would have had difficulty learning these are the Bell numbers.<sup>[3](https://oeis.org/EIStext.pdf)</sup> |
| Scale of use | A 2023 report describes the OEIS at 360,000 entries, a million visits a day, and 10,000 citations.<sup>[4](https://arxiv.org/abs/2301.03149)</sup> |
| Oldest recorded entries | The OEIS historical list runs from the Ishango bone (c. 20,000 bc, markings of unknown meaning) to a c. 2500 bc Babylonian table of numbers and their cubes and a c. 1900 bc Rhind Papyrus copy with calculations of π to 2 decimal digits.<sup>[5](https://oeis.org/wiki/Historical_sequences)</sup> |

## Number types

The broadest division is by set. Integers are whole numbers, positive, negative, or zero; the ring of integers has cardinal number ℵ0, meaning the integers can be placed in one-to-one correspondence with the natural numbers despite being infinite in both directions.<sup>[6](https://unvis.it/mathworld.wolfram.com/Integer.html)</sup> The meaning of the word "number" is often clear from context, whether it refers to a complex number, an integer, or a real number, and style conventions differ on details such as whether "and" appears in a spelled-out number name.<sup>[1](https://mathworld.wolfram.com/Number.html)</sup>

Within the integers, lists usually group numbers by a defining property rather than by size. Examples in the retrieved record include the nonnegative even numbers, defined by a(n) = 2n and carried in the OEIS as A005843, and the weird numbers, which are abundant but not pseudoperfect (number equal to sum of some of its proper divisors); finding weird numbers is a case of the [subset sum problem](https://www.edgepedia.org/subset-sum-problem), and the sequence is cataloged as A006037.<sup>[7](https://pub.tik.ee.ethz.ch/students/2022-FS/BA-2022-17.pdf)</sup><sup> • </sup><sup>[8](https://mathworld.wolfram.com/WeirdNumber.html)</sup> Research literature also defines families tied to other structures, such as F-perfect numbers, positive integers n satisfying \( \sum_{d \mid n,\, d < n} d^{2} = 3n \), introduced in work connecting perfect numbers and Fibonacci primes.<sup>[9](https://arxiv.org/abs/1310.0898)</sup>

## Mathematical constants

**Familiar entries.** The constant π, chosen as a symbol by the Welsh mathematician [William Jones](https://www.edgepedia.org/william-jones) nearly 314 years before a 2019 account, is described there as the most recognizable constant in mathematics. The number e, approximately 2.71828, is irrational; [Leonhard Euler](https://www.edgepedia.org/leonhard-euler) proved this about 20 years after the constant's discovery and popularized the notation that still carries his name.<sup>[10](https://time.com/5550847/pi-day-numbers/)</sup> Physics supplies further fixed values that appear on lists of notable numbers: the reduced [Planck constant](https://www.edgepedia.org/planck-constant) ħ, about 1.054 × 10<sup>−34</sup> in the units used for angular momentum, and the Boltzmann constant k, 8.617 × 10<sup>−5</sup> electron-volts per kelvin, the ratio between a particle's energy and its temperature.<sup>[10](https://time.com/5550847/pi-day-numbers/)</sup> Constants also relate to one another; Euler's identity, \( e^{i\pi} + 1 = 0 \), ties together e, i, and π in a single equation.<sup>[10](https://time.com/5550847/pi-day-numbers/)</sup>

## Catalogs: the OEIS

For integers, the standard reference list is the [On-Line Encyclopedia of Integer Sequences](https://www.edgepedia.org/on-line-encyclopedia-of-integer-sequences), founded from [Neil Sloane](https://www.edgepedia.org/neil-sloane)'s 1964 effort to collect integer sequences to help with his thesis.<sup>[11](https://oeis.org/A002572/a002572_3.pdf)</sup> The 1973 *Handbook of Integer Sequences* was the first published table of such sequences; its expanded successor, the *Encyclopedia of Integer Sequences*, grew into the online database.<sup>[3](https://oeis.org/EIStext.pdf)</sup> By 2023 the database held 360,000 entries, received a million visits a day, and had been cited 10,000 times, often with the comment "discovered thanks to the OEIS".<sup>[4](https://arxiv.org/abs/2301.03149)</sup> The site's own counter now reports 400,158 sequences.<sup>[2](https://oeis.org/)</sup>

**How entries are identified.** Each sequence carries an A-number, such as A001006 for the Motzkin numbers, a sequence studied since 1870.<sup>[4](https://arxiv.org/abs/2301.03149)</sup> Some entries also carry a 4-digit M-number, such as M1459, the identifier they held in the printed *Encyclopedia of Integer Sequences* by N. J. A. Sloane and [Simon Plouffe](https://www.edgepedia.org/simon-plouffe).<sup>[12](https://oeis.org/wiki/Style_Sheet)</sup> An entry lists initial terms (50 to 100 when available), a description, formulas, programs, and references; a companion b-file, named like b001006.txt, extends the term list, and entries can be plotted or played as sound.<sup>[4](https://arxiv.org/abs/2301.03149)</sup><sup> • </sup><sup>[13](https://neilsloane.com/doc/HIS50.Feb20.2023.pdf)</sup>

**How lists are searched.** The database supports several search modes: plain words, quoted phrases, comma-separated terms, field prefixes such as author: or formula:, a subseq: prefix that finds sequences containing the query as a subsequence, and a leading minus sign to exclude terms.<sup>[14](https://oeis.caseyjhand.com/)</sup><sup> • </sup><sup>[15](https://stackoverflow.com/questions/25340798/how-does-oeis-do-subsequence-search)</sup> Matching runs against the data line, the first terms of each entry, at most about 270 characters, so a run taken from far into a sequence is not found unless earlier terms are supplied.<sup>[14](https://oeis.caseyjhand.com/)</sup> Sequences may contain negative integers, in which case they are labeled with the keyword "sign"; sequences known to contain no negative integers carry the keyword "nonn".<sup>[12](https://oeis.org/wiki/Style_Sheet)</sup>

## Historical dimension

Lists of notable numbers reach back before written mathematics as usually understood. The OEIS historical sequence page links its entries to artifacts: the Ishango bone from about 20,000 bc with markings of unknown meaning, the Babylonian tablet BM 92698 from about 2500 bc containing a table of numbers and their cubes, and a copy preserved in the Rhind Papyrus from about 1900 bc with calculations of π equivalent to 2 decimal digits.<sup>[5](https://oeis.org/wiki/Historical_sequences)</sup> A later example is the 1410 Orloj astronomical clock by Jan Šindel and Mikuláš of Kadaň, associated with the sequence of its clock chimes.<sup>[5](https://oeis.org/wiki/Historical_sequences)</sup>

## What lists of numbers are for

The practical purpose of these catalogs is identification and retrieval.

## References

1. [Number, Wolfram MathWorld](https://mathworld.wolfram.com/Number.html)
2. [The On-Line Encyclopedia of Integer Sequences (OEIS), main page](https://oeis.org/)
3. [Preface text, *A Handbook of Integer Sequences* (OEIS EIS text)](https://oeis.org/EIStext.pdf)
4. ["A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149](https://arxiv.org/abs/2301.03149)
5. [Historical sequences, OeisWiki](https://oeis.org/wiki/Historical_sequences)
6. [Integer, Wolfram MathWorld](https://unvis.it/mathworld.wolfram.com/Integer.html)
7. [Algorithm Learning on OEIS, ETH Zürich student report](https://pub.tik.ee.ethz.ch/students/2022-FS/BA-2022-17.pdf)
8. [Weird Number, Wolfram MathWorld](https://mathworld.wolfram.com/WeirdNumber.html)
9. [Perfect numbers and Fibonacci primes, arXiv:1310.0898](https://arxiv.org/abs/1310.0898)
10. [Move Aside, Pi Day. These Six Numbers Are More Deserving of Celebration, Time](https://time.com/5550847/pi-day-numbers/)
11. [GUY2020, OEIS attached document on the history of the database](https://oeis.org/A002572/a002572_3.pdf)
12. [Style Sheet, OeisWiki](https://oeis.org/wiki/Style_Sheet)
13. ["A Handbook of Integer Sequences" Fifty Years Later (PDF), neilsloane.com](https://neilsloane.com/doc/HIS50.Feb20.2023.pdf)
14. [oeis-mcp-server, MCP server documentation](https://oeis.caseyjhand.com/)
15. [How does OEIS do subsequence search?, Stack Overflow](https://stackoverflow.com/questions/25340798/how-does-oeis-do-subsequence-search)

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*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Numbers and algebra › Arithmetic and number systems › Number systems*

*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026; Oct 25, 2026 · Last review: Oct 15, 2026*

*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*

License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license