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; Mathematica; DLMF; GAP; Maple; Magma; GitHub; nauty; gfun; MathOverflow; Traces; Sage-Combinat; Walnut; Macaulay2; BinaryTrees; PARI/GP; FindStat; SIGMA; Mace4; SINGULAR Cited in: 5,814 Documents Standard Articles 8 Publications describing the Software, including 8 Publications in zbMATH Year The On-Line Encyclopedia of Integer Sequences. Zbl 1439.11001Sloane, Neil J. A. 2018 The On-Line Encyclopedia of Integer Sequences. Zbl 1274.11001Sloane, N. J. A. 2013 The On-Line Encyclopedia of Integer Sequences. (Abstract). Zbl 1159.11327Sloane, Neil J. A. 2007 The On-Line Encyclopedia of Integer Sequences. Zbl 1044.11108Sloane, N. J. A. 2003 My favorite integer sequences. Zbl 1049.11026Sloane, N. J. A. 1999 The encyclopedia of integer sequences. Incl. 1 IBM/MS-DOS disk. (3.5). Zbl 0845.11001Sloane, N. J. A.; Plouffe, Simon 1995 An on-line version of “The Encyclopedia of Integer Sequences”. Zbl 0815.11001Sloane, N. J. A. 1994 A handbook of integer sequences. Zbl 0286.10001Sloane, N. J. A. 1973 all top 5 Cited by 6,317 Authors 117 Mansour, Toufik 69 Shattuck, Mark A. 54 Barry, Paul 50 Shallit, Jeffrey Outlaw 46 Ramírez, José Luis 41 Baril, Jean-Luc 40 Merca, Mircea 40 Sloane, Neil James Alexander 33 Prodinger, Helmut 32 Kitaev, Sergey 32 Rinaldi, Simone 30 Luca, Florian 30 Zeilberger, Doron 26 Tenner, Bridget Eileen 25 Novelli, Jean-Christophe 25 Sun, Zhi-Wei 24 Ballantine, Cristina M. 24 Belbachir, Hacene 24 Ferrari, Luca 24 Ma, Shi-Mei 24 Munagi, Augustine O. 23 Flórez, Rigoberto 23 Komatsu, Takao 23 Thibon, Jean-Yves 22 Giraudo, Samuele 22 Shapiro, Louis W. 20 Došlić, Tomislav 20 Knopfmacher, Arnold 20 Morales, Alejandro Henry 20 Pak, Igor 19 Dilcher, Karl 19 Goy, Taras P. 19 Kimberling, Clark H. 19 Munarini, Emanuele 19 Yang, Shengliang 18 Allouche, Jean-Paul Simon 18 Pinzani, Renzo 18 Sellers, James Allen 18 Soykan, Yüksel 17 Andrews, George Eyre 17 Claesson, Anders 17 Elizalde, Sergi 17 Pudwell, Lara K. 17 Szalay, László 17 Wagner, Stephan Georg 17 Yeh, Yeong-Nan 16 Bényi, Beáta 16 Callan, David 16 Cheon, Gi-Sang 16 Eu, Sen-Peng 16 He, Tian-Xiao 16 Kirgizov, Sergey 16 Mező, István 16 Németh, László 15 Barequet, Gill 15 Billey, Sara C. 15 Blecher, Aubrey 15 Bouvel, Mathilde 15 Deutsch, Emeric 15 Gil, Juan B. 15 Hetyei, Gábor 15 Hivert, Florent 15 Lin, Zhicong 15 Schork, Matthias 15 Sokal, Alan D. 15 Yang, Lin 14 Han, Guo-Niu 14 Rampersad, Narad 14 Remmel, Jeffrey Brian 14 Rowland, Eric S. 14 Zhu, Baoxuan 13 Bagdasar, Ovidiu Dumitru 13 Barbero, Stefano 13 Barcucci, Elena 13 Bernini, Antonio 13 Defant, Colin 13 Dekking, Frederik Michel 13 Ericksen, Larry 13 Griffiths, Martin 13 Murru, Nadir 13 Pongsriiam, Prapanpong 13 Ricci, Paolo Emilio 13 Shevelev, Vladimir Samuil 13 Silimbani, Matteo 13 Sun, Yidong 13 Tóth, László 12 Barnabei, Marilena 12 Bonetti, Flavio 12 Campbell, John Maxwell 12 Cerruti, Umberto 12 Chen, William Yong-Chuan 12 Fu, Tung-Shan 12 Kauers, Manuel 12 Marberg, Eric 12 Panova, Greta 12 Pergola, Elisa 12 Sapounakis, Aristidis 12 Tasoulas, Ioannis 12 Togbé, Alain 12 Zeng, Jiang ...and 6,217 more Authors all top 5 Cited in 647 Serials 1,136 Journal of Integer Sequences 250 Discrete Mathematics 187 The Electronic Journal of Combinatorics 151 Integers 124 European Journal of Combinatorics 122 Journal of Combinatorial Theory. Series A 118 Advances in Applied Mathematics 108 Discrete Applied Mathematics 99 Theoretical Computer Science 85 Linear Algebra and its Applications 68 Annals of Combinatorics 65 Séminaire Lotharingien de Combinatoire 64 Journal of Algebraic Combinatorics 60 The Ramanujan Journal 58 Journal of Number Theory 58 Journal of High Energy Physics 52 Journal of Algebra 49 The Australasian Journal of Combinatorics 43 The Fibonacci Quarterly 41 Graphs and Combinatorics 40 American Mathematical Monthly 38 Journal of Physics A: Mathematical and Theoretical 37 Journal of Difference Equations and Applications 36 Advances in Mathematics 32 Enumerative Combinatorics and Applications 29 Mathematics of Computation 29 International Journal of Number Theory 28 Experimental Mathematics 27 Proceedings of the American Mathematical Society 27 SIAM Journal on Discrete Mathematics 27 Discrete Mathematics and Theoretical Computer Science. DMTCS 25 Transactions of the American Mathematical Society 25 Order 23 Journal of Symbolic Computation 22 Discrete & Computational Geometry 22 Aequationes Mathematicae 21 Algebraic Combinatorics 20 Journal of Mathematical Analysis and Applications 20 Mathematics Magazine 20 The Mathematical Intelligencer 20 Quaestiones Mathematicae 19 Applied Mathematics and Computation 19 Combinatorial Theory 18 Information Processing Letters 18 Semigroup Forum 18 Algorithmica 18 Designs, Codes and Cryptography 18 The College Mathematics Journal 17 Rocky Mountain Journal of Mathematics 17 Monatshefte für Mathematik 17 Journal of Statistical Mechanics: Theory and Experiment 17 DML. Discrete Mathematics Letters 16 Mediterranean Journal of Mathematics 16 International Journal of Advances in Applied Mathematics and Mechanics 15 Journal of Statistical Physics 15 Acta Arithmetica 15 Results in Mathematics 14 Journal of Mathematical Physics 14 Journal of Mathematical Sciences (New York) 14 Applicable Analysis and Discrete Mathematics 14 Ars Mathematica Contemporanea 13 Communications in Mathematical Physics 13 The Mathematical Gazette 13 Boletín de la Sociedad Matemática Mexicana. Third Series 12 Indian Journal of Pure & Applied Mathematics 12 Journal of Pure and Applied Algebra 12 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 12 Discrete Mathematics, Algorithms and Applications 11 Bulletin of the Australian Mathematical Society 11 Linear and Multilinear Algebra 11 Mathematische Zeitschrift 11 Journal of Knot Theory and its Ramifications 11 Congressus Numerantium 11 Journal of Mathematical Chemistry 11 Journal of Discrete Mathematical Sciences & Cryptography 11 The Art of Discrete and Applied Mathematics 10 International Journal of Mathematical Education in Science and Technology 10 Journal of Mathematical Biology 10 Nuclear Physics. B 10 Combinatorica 10 Random Structures & Algorithms 10 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 10 Finite Fields and their Applications 10 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 10 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 10 RAIRO. Theoretical Informatics and Applications 10 SIAM Journal on Applied Algebra and Geometry 10 Electronic Research Archive 9 Israel Journal of Mathematics 9 Chaos, Solitons and Fractals 9 Mathematica Slovaca 9 Computational Geometry 9 Expositiones Mathematicae 9 Journal de Théorie des Nombres de Bordeaux 9 Annales Mathematicae Silesianae 9 Contributions to Discrete Mathematics 9 Mathematics in Computer Science 9 Involve 9 Asian-European Journal of Mathematics 9 PUMP Journal of Undergraduate Research ...and 547 more Serials all top 5 Cited in 62 Fields 3,196 Combinatorics (05-XX) 2,538 Number theory (11-XX) 632 Computer science (68-XX) 323 Group theory and generalizations (20-XX) 299 Linear and multilinear algebra; matrix theory (15-XX) 258 Special functions (33-XX) 229 Convex and discrete geometry (52-XX) 218 Order, lattices, ordered algebraic structures (06-XX) 208 Probability theory and stochastic processes (60-XX) 174 Quantum theory (81-XX) 173 Algebraic geometry (14-XX) 167 Associative rings and algebras (16-XX) 111 Information and communication theory, circuits (94-XX) 108 Dynamical systems and ergodic theory (37-XX) 101 Numerical analysis (65-XX) 99 Commutative algebra (13-XX) 94 Operations research, mathematical programming (90-XX) 91 Statistical mechanics, structure of matter (82-XX) 91 Biology and other natural sciences (92-XX) 88 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 81 Nonassociative rings and algebras (17-XX) 73 General and overarching topics; collections (00-XX) 71 Geometry (51-XX) 69 Functions of a complex variable (30-XX) 69 Manifolds and cell complexes (57-XX) 61 Real functions (26-XX) 58 Category theory; homological algebra (18-XX) 56 Mathematical logic and foundations (03-XX) 53 Difference and functional equations (39-XX) 53 Statistics (62-XX) 51 Ordinary differential equations (34-XX) 50 Harmonic analysis on Euclidean spaces (42-XX) 49 Sequences, series, summability (40-XX) 42 Approximations and expansions (41-XX) 35 Functional analysis (46-XX) 35 Mathematics education (97-XX) 34 Integral transforms, operational calculus (44-XX) 33 Algebraic topology (55-XX) 30 History and biography (01-XX) 28 Relativity and gravitational theory (83-XX) 26 Field theory and polynomials (12-XX) 23 Partial differential equations (35-XX) 23 General topology (54-XX) 22 Differential geometry (53-XX) 21 Topological groups, Lie groups (22-XX) 21 Measure and integration (28-XX) 21 Operator theory (47-XX) 18 General algebraic systems (08-XX) 18 Systems theory; control (93-XX) 15 Mechanics of particles and systems (70-XX) 12 Several complex variables and analytic spaces (32-XX) 12 Global analysis, analysis on manifolds (58-XX) 8 Abstract harmonic analysis (43-XX) 7 Fluid mechanics (76-XX) 6 Integral equations (45-XX) 5 \(K\)-theory (19-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 2 Potential theory (31-XX) 2 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Mechanics of deformable solids (74-XX) 1 Geophysics (86-XX) Citations by Year