一個 序列,其項為 整數。關於這類序列最完整的印刷參考文獻是 Sloane (1973) 及其更新版 Sloane 和 Plouffe (1995)。Neil Sloane 在一個名為“整數序列線上百科全書”的、內容大大擴充套件的線上百科全書中維護著這兩部著作中的序列 (http://www.research.att.com/~njas/sequences/)。在這個列表中,序列透過唯一的 6 位 數字 A 編號來標識。Sloane 和 Plouffe (1995) 中出現的序列按字典順序排列,並用 4 位 數字 M 編號標識,而 Sloane (1973) 中出現的序列用 4 位 數字 N 編號標識。要透過電子郵件查詢序列,請傳送訊息至 mailto:sequences@research.att.com 或 mailto:superseeker@research.att.com,其中包含 以下形式 的行lookup 5 14 42 132 ...(注意必須使用空格代替逗號)。
整數序列可以透過多種技術進行分析(Sloane 和 Plouffe 1995,第 26 頁),包括應用資料壓縮演算法(Bell 等人 1990)、計算 離散傅立葉變換(Loxton 1989),或者搜尋連線項的 線性遞推方程 或生成它們的 生成函式。還有大量將整數序列彼此關聯的變換,包括 尤拉變換、指數變換、莫比烏斯變換 等(Bower,Sloane)。
某些序列項的閉合形式可以在 Wolfram 語言 中使用以下命令找到FindSequenceFunction[seq]。
在電視犯罪劇集 NUMB3RS 第二季的劇集“散射”(2006 年)中,數學天才 Charlie Eppes 向他的學生提出了一個識別整數序列的問題,其中一名學生使用 Sloane 的整數序列線上百科全書找到了它。
另請參閱
組合數學,
連續數字序列,
生成函式,
整數陣列,
整數序列素數,
線性遞推方程,
莫比烏斯變換,
數,
帕多瓦序列,
序列,
Smarandache 序列
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參考文獻
Aho, A. V. and Sloane, N. J. A. "Some Doubly Exponential Sequences." Fib. Quart. 11, 429-437, 1973.Bell, T. C.; Cleary, J. G.; and Witten, I. H. Text Compression. Englewood Cliffs, NJ: 1990.Bernstein, M. and Sloane, N. J. A. "Some Canonical Sequences of Integers." Linear Algebra Appl. 226//228, 57-72, 1995.Bower, C. G. "Further Transformations of Integer Sequences." http://www.research.att.com/~njas/sequences/transforms2.html.Cameron, P. J. "Some Sequences of Integers." Disc. Math. 75, 89-102, 1989.Ding, C.; Helleseth, T.; and Niederreiter, H. (Eds.). Sequences and Their Applications: Proceedings of SETA' 98. New York: Springer-Verlag, 1999.Erdős, P.; Sárkőzy, E.; and Szemerédi, E. "On Divisibility Properties of Sequences of Integers." In Number Theory, Colloq. Math. Soc. János Bolyai, Vol. 2. Amsterdam, Netherlands: North-Holland, pp. 35-49, 1970.Guy, R. K. "Sequences of Integers." Ch. E in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 199-239, 1994.Kimberling, C. "Integer Sequences and Arrays." http://faculty.evansville.edu/ck6/integer/.Krattenthaler, C. "RATE: A Mathematica Guessing Machine." http://radon.mat.univie.ac.at/People/kratt/rate/rate.html.Loxton, J. H. "Spectral Studies of Automata." In Irregularities of Partitions (Ed. G. Halász and V. T. Sós). New York: Springer-Verlag, pp. 115-128, 1989.Ostman, H. Additive Zahlentheorie I, II. Heidelberg, Germany: Springer-Verlag, 1956.Pegg, E. Jr. "Math Games: Sequence Pictures." Dec. 8, 2003. http://www.maa.org/editorial/mathgames/mathgames_12_08_03.html.Pegg, E. Jr. and Weisstein, E. W. "Seven Mathematical Tidbits." Headline News. Nov. 8, 2004. https://mathworld.tw/news/2004-11-08/seventidbits/#3.Peterson, I. "MathTrek: Sequence Puzzles." May 17, 2003. http://www.sciencenews.org/20030517/mathtrek.asp.Petit, S. "Encyclopedia of Combinatorial Structures." http://algo.inria.fr/encyclopedia/.Pomerance, C. and Sárközy, A. "Combinatorial Number Theory." In Handbook of Combinatorics (Ed. R. Graham, M. Grötschel, and L. Lovász). Amsterdam, Netherlands: North-Holland, 1994.Ruskey, F. "The (Combinatorial) Object Server." http://www.theory.csc.uvic.ca/~cos/.Sloane, N. J. A. A Handbook of Integer Sequences. Boston, MA: Academic Press, 1973.Sloane, N. J. A. "Find the Next Term." J. Recr. Math. 7, 146, 1974.Sloane, N. J. A. "An On-Line Version of the Encyclopedia of Integer Sequences." Electronic J. Combinatorics 1, No. 1, F1, 1-5, 1994. http://www.combinatorics.org/Volume_1/Abstracts/v1i1f1.html.Sloane, N. J. A. "An On-Line Version of the Encyclopedia of Integer Sequences." http://www.research.att.com/~njas/sequences/eisonline.html.Sloane, N. J. A. "Some Important Integer Sequences." In CRC Standard Mathematical Tables and Formulae. (Ed. D. Zwillinger). Boca Raton, FL: CRC Press, 1995.Sloane, N. J. A. "The On-Line Encyclopedia of Integer Sequences." Not. Amer. Math. Soc. 50, 912-915, 2003.Sloane, N. J. A. "Transformation of Integer Sequences." http://www.research.att.com/~njas/sequences/transforms.html.Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, 1995.Stephan, R. "Prove or Disprove. 100 Conjectures from the OEIS." 27 Sep 2004. http://www.arxiv.org/abs/math.CO/0409509/.Stephan, R. "Do you have a comment or news on conjectures in the article math.CO/0409509?" http://www.ark.in-berlin.de/conj.txt.Stöhr, A. "Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe I, II." J. reine angew. Math. 194, 40-65 and 111-140, 1955.Turán, P. (Ed.). Number Theory and Analysis: A Collection of Papers in Honor of Edmund Landau (1877-1938). New York: Plenum Press, 1969.在 中被引用
整數序列
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Weisstein, Eric W. "整數序列。" 來自 —— 資源。 https://mathworld.tw/IntegerSequence.html
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