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整數序列


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.commailto: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。


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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.

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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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