My Favorite Integer Sequences

By N. Sloane. Sequences and Their Applications, 2002

578 citations recorded by the source corpus.

This paper gives a brief description of the author’s database of integer sequences, now over 35 years old, together with a selection of a few of the most interesting sequences in the table. Many unsolved problems are mentioned.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/064f8e1c3792be2ff45e070a30e3cb9303fa7978

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In Computational Theory and Mathematics

In Electrical and Electronic Engineering

Citations in the corpus

Advanced Determinant Calculus: A Complement (2005, background): “So I consulted the fabulous On-Line Encyclopedia of Integer Sequences (http://www.research.att.com/~njas/sequences/Seis.html), originally created by Neil Sloane and Simon Plouffe [160], and since many years continuously further developed by Sloane and his team [159].”
On the independence complex of square grids (2006, methodology): “We refer the reader to the entry A006506 in the On-line Encyclopedia of Integer Sequences for more details [11].”
Analysis of some new partition statistics (2006, methodology): “KNOPFMACHER This is sequence A066898 in [9] where it appears under the heading, total number of even parts in all partitions of n.”
Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review (2016, unknown): “(6) For orders p = {1, 2, 3, 4, 5, 6}, j ranges from 1 to ap = {1, 1, 2, 4, 9, 20}, respectively (see Sloane and Plouffe [401]; sequence A000081, formerly M1180 and N0454).”
On Generalizations of the Stirling Number Triangles (2000, background): “in the notation of [3], or S (m) n in [1], or sequence A008277 in the database [10]) can be defined by E n x ≡ (x dx) n = n”
Korat: automated testing based on Java predicates (2002, background): “ForBinaryTree , LinkedList , TreeMap , andHashSet (5), the numbers of nonisomorphic structures appear in the Sloane’s On-Line Encyclopedia of Integer Sequences [31].”
Deep Learning for Symbolic Mathematics (2019, methodology): “n= C np n 2 L n+1 ˇ 4n n p ˇn pn 2 L n+1 with C n= 1 n+1 2n n If p 1 >0, expressions are unary-binary trees, and the number of trees with ninternal nodes is the n-th large Schroeder number S n(Sloane, 1996). It can be computed by recurrence using the following equation: (n+1)S n= 3(2n 1)S n 1 (”
Analytic Combinatorics (2009, background): “There even ex ists nowadays a huge On-line Encyclopedia of Integer Sequences (EIS) due to Sloane that is available in electronic form [543] (see also an earlier book by Sloane and Plouffe [544]) and contains more than 100 000 sequences.”
Elliptic integral evaluations of Bessel moments and applications (2008, background): “lead to explicit expressions for the integer sequences in entries A2897, A2896 and A2895, respectively, of the on-line version of [64].”