The On-Line Encyclopedia of Integer Sequences

  title={The On-Line Encyclopedia of Integer Sequences},
  author={N. J. A. Sloane},
  journal={Electron. J. Comb.},
  • N. Sloane
  • Published 24 December 2003
  • Computer Science
  • Electron. J. Comb.
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences. It is freely available on the Web ( 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… 
The encyclopedia of integer sequences
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
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
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.
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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
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A note on p-Ascent Sequences
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
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.
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
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
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


The encyclopedia of integer sequences
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.
Some canonical sequences of integers
Arithmetical properties of permutations of integers
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
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
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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
  • M. O'keefeB. Hyde
  • Geology
    Philosophical 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
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
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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
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