# The On-Line Encyclopedia of Integer Sequences

@article{Sloane1994TheOE, title={The On-Line Encyclopedia of Integer Sequences}, author={N. J. A. Sloane}, journal={Electron. J. Comb.}, year={1994}, volume={1} }

The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences. It is freely available on the Web (http://www.research.att.com/~njas/sequences/) and is widely used.
There are several ways in which it benefits research: 1 It serves as a dictionary, to tell the user what is known about a particular sequence. There are hundreds of papers which thank the OEIS for assistance in this way.
1 The associated Sequence Fans mailing list is a worldwide network…

## 5,754 Citations

The encyclopedia of integer sequences

- Computer Science
- 1995

This book presents methods for Computer Investigation of Sequences, a method for hand analysis of sequences, and some of the methods used in this work, as well as suggestions for further study.

Disquisitiones Arithmeticae and online sequence A108345

- Mathematics
- 2010

Let g be the element that is the sum of x^(n^2) for n >= 0 of A=Z/2[[x]], and let B consist of all n for which the coefficient of x^n in 1/g is 1. (The elements of B are the entries 0, 1, 2, 3, 5, 7,…

Experimental methods applied to the computation of integer sequences

- Computer Science, Mathematics
- 2009

The experimental method is applied to certain problems in number theory and combinatorics to understand certain integer sequences, and the recurrence an=an-1 +gcdn,an- 1 , which is shown to generate primes in a certain sense.

Fibonacci-like sequences and shift spaces in symbolic dynamics

- Computer Science
- 2008

How many of these problems may be expressed and solved in terms of Fibonacci-like recurrent relations in a simple, intuitive and amenable way are shown and the limit ratios of such sequences to the topological entropy of the corresponding shift space are related.

On Hultman numbers

- Mathematics
- 2007

Finding a sequence of transpositions that transforms a given permutation into the identity permutation and is of the shortest possible length is an important problem in bioinformatics. Here, a…

A note on p-Ascent Sequences

- Mathematics
- 2017

Ascent sequences were introduced by Bousquet-Melou, Claesson, Dukes, and Kitaev in [1], who showed that ascent sequences of length n are in 1-to-1 correspondence with (2+2)-free posets of size n. In…

On Curling Numbers of Integer Sequences

- MathematicsArXiv
- 2012

This paper determines how far a sequence of n 2's and 3's can extend before reaching a 1, conjecturally for n <= 80, and investigates several related combinatorial problems, such as finding c(n,k), the number of binary sequences of length n and curling number k, and t( n,i), theNumber of sequences oflength n which extend for i steps before reach a 1.

On the ubiquity of the ruler sequence.

- Mathematics
- 2020

The ruler function or the Gros sequence is a classical infinite integer sequence that is underlying some interesting mathematical problems. In this paper, we provide four new problems containing this…

Formula Semantification and Automated Relation Finding in the On-Line Encyclopedia for Integer Sequences

- Computer ScienceICMS
- 2016

This paper provides a partial parser for the OEIS that leverages the fact that, in practice, the syntax used in its formulas is fairly regular, and imports the result into OMDoc to make the O EIS accessible to O MDoc-based knowledge management applications.

Discriminators and k-Regular Sequences

- MathematicsIntegers
- 2016

The discriminator of an integer sequence s = (s(i))i≥0, introduced by Arnold, Benkoski, and McCabe in 1985, is the map Ds(n) that sends n ≥ 1 to the least positive integer m such that the n numbers…

## References

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The encyclopedia of integer sequences

- Computer Science
- 1995

This book presents methods for Computer Investigation of Sequences, a method for hand analysis of sequences, and some of the methods used in this work, as well as suggestions for further study.

Arithmetical properties of permutations of integers

- Mathematics
- 1983

For the finite case let a1 , a 2 , . . ., an be a permutation of the integers 1, 2, . . ., n and for the infinite case let a 1 , a2 , . . ., ai , . . . be a permutation of all positive integers .…

The First 50 Million Prime Numbers

- Mathematics
- 1977

I would like to tell you today about a subject which, although I have not worked in it myself, has always extraordinarily captivated me, and which has fascinated mathematicians from the earliest…

What Is Enumerative Combinatorics

- Mathematics
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The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Usually are given an infinite class of finite sets S i where i ranges over some index set I…

Handbook of Number Theory I

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Preface. Basic Symbols. Basic Notations. I. Euler's phi-function. II. The arithmetical function d(n), its generalizations and its analogues. III. Sum-of-divisors function, generalizations, analogues…

Plane nets in crystal chemistry

- GeologyPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- 1980

In the present paper we consider not only the simplest periodic nets (such as arise from the equivalent circle packings of Niggli, Fejes Toth and others) but also less regular ones, ignored by…

Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products

- Mathematics
- 1948

This note improves, in two respects, the results of §3.6 of my paper The hyper surface cross ratio. There it is shown that the number cn of independent hypersurface cross ratios that can be formed of…

Pi, Euler numbers, and asymptotic expansions

- Mathematics
- 1989

Gregory’s series for π, truncated at 500,000 terms, gives to forty places
$$4\sum\limits_{k = 1}^{500.000} {\frac{{{{\left( { - 1} \right)}^{k - 1}}}}{{2k - 1}}} =…

GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable

- MathematicsTOMS
- 1994

We describe the GFUN package which contains functions for manipulating sequences, linear recurrences, or differential equations and generating functions of various types. This article is intended…