## OEIS

 swMATH ID: 7248 Software Authors: Sloane, Neil J. A.; The OEIS Foundation Inc. Description: The On-Line Encyclopedia of Integer Sequence. The main use for the OEIS is to identify a number sequence that you have come across, perhaps in your work, while reading a book, or in a quiz, etc. For example, you discover what you think may be a new algorithm for checking that a file of medical records is in the correct order. (Perhaps you are a computer scientist or someone working in information science.) To handle files of 1, 2, 3, 4, ... records, your algorithm takes 0, 1, 3, 5, 9, 11, 14, 17, 25, ... steps. How can you check if someone has discovered this algorithm before? You decide to ask the OEIS if this sequence has appeared before in the scientific literature. You go the OEIS web site, enter the numbers you have calculated, and click ”Submit”. The reply tells you that this is sequence A3071, which is the number of steps needed for ”sorting by list merging”, a well-known algorithm. The entry directs you to Section 5.3.1 of Volume 3 of D. E. Knuth, ”The Art of Computer Programming”, where you find your algorithm described. The entry even gives an explicit formula for the nth term. You decide not to apply for a patent! The OEIS web site includes a list of well over 3000 books and articles that have acknowledged help from the OEIS. Homepage: http://oeis.org/?language=english Related Software: SageMath; GAP; Mathematica; DLMF; Maple; Magma; nauty; GitHub; gfun; Sage-Combinat; Macaulay2; MathOverflow; Traces; BinaryTrees; FindStat; PARI/GP; OPQ; AARON; GJsqfree; GJSAW Cited in: 4,442 Publications
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### Cited by 4,873 Authors

 101 Mansour, Toufik 58 Shattuck, Mark A. 51 Barry, Paul 37 Sloane, Neil James Alexander 33 Shallit, Jeffrey O. 32 Merca, Mircea 30 Rinaldi, Simone 28 Baril, Jean-Luc 27 Kitaev, Sergey 27 Luca, Florian 24 Ramírez, José Luis 23 Prodinger, Helmut 23 Zeilberger, Doron 22 Ferrari, Luca 22 Shapiro, Louis W. 22 Tenner, Bridget Eileen 21 Ma, Shi-Mei 21 Novelli, Jean-Christophe 20 Belbachir, Hacene 20 Thibon, Jean-Yves 19 Giraudo, Samuele 19 Munagi, Augustine O. 18 Kimberling, Clark H. 18 Munarini, Emanuele 17 Allouche, Jean-Paul Simon 17 Dilcher, Karl 17 Morales, Alejandro Henry 16 Cheon, Gi-Sang 16 Flórez, Rigoberto 16 Pinzani, Renzo 15 Knopfmacher, Arnold 15 Mező, István 15 Pak, Igor 15 Sun, Zhi-Wei 15 Yeh, Yeong-Nan 14 Deutsch, Emeric 14 Došlić, Tomislav 14 Elizalde, Sergi 14 Hetyei, Gábor 14 Hivert, Florent 14 Pudwell, Lara K. 14 Remmel, Jeffrey Brian 14 Sellers, James Allen 13 Billey, Sara C. 13 Ericksen, Larry 13 Eu, Sen-Peng 13 Griffiths, Martin 13 Kirgizov, Sergey 13 Ricci, Paolo Emilio 13 Schork, Matthias 13 Shevelev, Vladimir Samuil 13 Wagner, Stephan G. 12 Bagdasar, Ovidiu Dumitru 12 Barbero, Stefano 12 Callan, David 12 Goy, Taras P. 12 Han, Guo-Niu 12 Murru, Nadir 12 Panova, Greta 12 Pergola, Elisa 12 Rowland, Eric S. 11 Andrews, George Eyre 11 Barcucci, Elena 11 Bényi, Beáta 11 Bernini, Antonio 11 Bouvel, Mathilde 11 Cerruti, Umberto 11 Chen, William Yong-Chuan 11 Janjić, Milan 11 Klavžar, Sandi 11 Komatsu, Takao 11 Marques, Diego 11 Sapounakis, Aristidis 11 Silimbani, Matteo 11 Tóth, László 11 Tsikouras, Panagiotis 11 Vatter, Vincent Russell 11 Yang, Shengliang 10 Baake, Michael 10 Ballantine, Cristina M. 10 Barnabei, Marilena 10 Blecher, Aubrey 10 Bonetti, Flavio 10 Borwein, Jonathan Michael 10 Claesson, Anders 10 Disanto, Filippo 10 Fu, Tung-Shan 10 Gil, Juan B. 10 Marberg, Eric 10 Ruskey, Frank 10 Sondow, Jonathan D. 10 Sun, Yidong 10 Tasoulas, Ioannis 10 Wanless, Ian M. 9 Andrica, Dorin 9 Barequet, Gill 9 Čerin, Zvonko Tomislav 9 Dekking, Frederik Michel 9 Frosini, Andrea 9 Gulliver, Thomas Aaron ...and 4,773 more Authors
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### Cited in 556 Serials

 1,026 Journal of Integer Sequences 207 Discrete Mathematics 145 The Electronic Journal of Combinatorics 114 Integers 105 European Journal of Combinatorics 94 Journal of Combinatorial Theory. Series A 90 Discrete Applied Mathematics 82 Advances in Applied Mathematics 79 Theoretical Computer Science 67 Linear Algebra and its Applications 56 Journal of Algebraic Combinatorics 53 Annals of Combinatorics 47 Séminaire Lotharingien de Combinatoire 47 The Ramanujan Journal 46 Journal of Number Theory 42 Journal of Algebra 40 Journal of High Energy Physics 37 The Australasian Journal of Combinatorics 36 Graphs and Combinatorics 28 American Mathematical Monthly 28 Advances in Mathematics 28 Journal of Difference Equations and Applications 24 The Fibonacci Quarterly 23 International Journal of Number Theory 22 Mathematics of Computation 22 Proceedings of the American Mathematical Society 22 Transactions of the American Mathematical Society 21 SIAM Journal on Discrete Mathematics 20 Experimental Mathematics 19 Order 18 Applied Mathematics and Computation 17 Information Processing Letters 17 Journal of Symbolic Computation 17 Discrete & Computational Geometry 16 The Mathematical Intelligencer 16 Semigroup Forum 16 Designs, Codes and Cryptography 15 Algorithmica 14 Acta Arithmetica 14 Aequationes Mathematicae 14 Journal of Statistical Mechanics: Theory and Experiment 14 Algebraic Combinatorics 13 Journal of Mathematical Analysis and Applications 13 Journal of Statistical Physics 13 Rocky Mountain Journal of Mathematics 13 Monatshefte für Mathematik 13 Discrete Mathematics and Theoretical Computer Science. DMTCS 13 Journal of Physics A: Mathematical and Theoretical 12 The Mathematical Gazette 12 Mediterranean Journal of Mathematics 12 Applicable Analysis and Discrete Mathematics 12 Ars Mathematica Contemporanea 11 Communications in Mathematical Physics 11 Journal of Mathematical Sciences (New York) 11 Congressus Numerantium 11 The College Mathematics Journal 11 DML. Discrete Mathematics Letters 10 Journal of Pure and Applied Algebra 10 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 10 Journal of Discrete Mathematical Sciences & Cryptography 9 International Journal of Mathematical Education in Science and Technology 9 Journal of Mathematical Biology 9 Journal of Mathematical Physics 9 Chaos, Solitons and Fractals 9 Mathematics Magazine 9 Results in Mathematics 9 Discrete Mathematics, Algorithms and Applications 9 Combinatorial Theory 8 Bulletin of the Australian Mathematical Society 8 Journal of Statistical Planning and Inference 8 Mathematische Zeitschrift 8 Combinatorica 8 Journal de Théorie des Nombres de Bordeaux 8 Filomat 8 Journal of Mathematical Chemistry 8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 8 SIAM Journal on Applied Algebra and Geometry 8 Electronic Research Archive 7 Nuclear Physics. B 7 Colloquium Mathematicum 7 Czechoslovak Mathematical Journal 7 Applied Mathematics Letters 7 Expositiones Mathematicae 7 Boletín de la Sociedad Matemática Mexicana. Third Series 7 Central European Journal of Mathematics 7 Advances in Difference Equations 7 Mathematics in Computer Science 7 Asian-European Journal of Mathematics 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 International Journal of Advances in Applied Mathematics and Mechanics 6 Indian Journal of Pure & Applied Mathematics 6 Israel Journal of Mathematics 6 Mathematical Notes 6 Journal of the Korean Mathematical Society 6 Quaestiones Mathematicae 6 Acta Applicandae Mathematicae 6 Elemente der Mathematik 6 Journal of Knot Theory and its Ramifications 6 Turkish Journal of Mathematics 6 Finite Fields and their Applications ...and 456 more Serials
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### Cited in 61 Fields

 2,433 Combinatorics (05-XX) 1,976 Number theory (11-XX) 474 Computer science (68-XX) 245 Group theory and generalizations (20-XX) 221 Linear and multilinear algebra; matrix theory (15-XX) 201 Special functions (33-XX) 158 Order, lattices, ordered algebraic structures (06-XX) 154 Convex and discrete geometry (52-XX) 145 Probability theory and stochastic processes (60-XX) 129 Associative rings and algebras (16-XX) 123 Quantum theory (81-XX) 120 Algebraic geometry (14-XX) 88 Information and communication theory, circuits (94-XX) 82 Numerical analysis (65-XX) 76 Dynamical systems and ergodic theory (37-XX) 67 Operations research, mathematical programming (90-XX) 67 Biology and other natural sciences (92-XX) 66 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 61 Nonassociative rings and algebras (17-XX) 60 Commutative algebra (13-XX) 60 Statistical mechanics, structure of matter (82-XX) 58 General and overarching topics; collections (00-XX) 52 Geometry (51-XX) 49 Real functions (26-XX) 45 Functions of a complex variable (30-XX) 44 Manifolds and cell complexes (57-XX) 42 Category theory; homological algebra (18-XX) 42 Harmonic analysis on Euclidean spaces (42-XX) 39 Mathematical logic and foundations (03-XX) 37 Sequences, series, summability (40-XX) 34 Difference and functional equations (39-XX) 33 Ordinary differential equations (34-XX) 33 Statistics (62-XX) 31 Approximations and expansions (41-XX) 29 Integral transforms, operational calculus (44-XX) 24 Algebraic topology (55-XX) 23 History and biography (01-XX) 23 Mathematics education (97-XX) 21 Functional analysis (46-XX) 21 Differential geometry (53-XX) 20 Field theory and polynomials (12-XX) 20 General topology (54-XX) 19 Relativity and gravitational theory (83-XX) 18 Partial differential equations (35-XX) 15 Measure and integration (28-XX) 14 Topological groups, Lie groups (22-XX) 14 Systems theory; control (93-XX) 12 General algebraic systems (08-XX) 12 Operator theory (47-XX) 11 Mechanics of particles and systems (70-XX) 10 Global analysis, analysis on manifolds (58-XX) 8 Several complex variables and analytic spaces (32-XX) 5 Integral equations (45-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Fluid mechanics (76-XX) 3 $$K$$-theory (19-XX) 3 Abstract harmonic analysis (43-XX) 1 Potential theory (31-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX)