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}
}
  • 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 (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… 
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On Hultman numbers
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References

SHOWING 1-10 OF 51 REFERENCES
The encyclopedia of integer sequences
TLDR
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
What Is Enumerative Combinatorics
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
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'keefe, B. 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
Pi, Euler numbers, and asymptotic expansions
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
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