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Search: id:A054639
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| A054639 |
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Queneau numbers: numbers n such that the Queneau-Daniel permutation {1, 2, 3, ..., n} -> {n, 1, n-1, 2, n-2, 3, ...} is of order n. |
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3
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| 1, 2, 3, 5, 6, 9, 11, 14, 18, 23, 26, 29, 30, 33, 35, 39, 41, 50, 51, 53, 65, 69, 74, 81, 83, 86, 89, 90, 95, 98, 99, 105, 113, 119, 131, 134, 135, 146, 155, 158, 173, 174, 179, 183, 186, 189, 191, 194, 209, 210, 221, 230, 231, 233, 239
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The troubadour Arnaut Daniel composed sestinas based on the permutation 123456 -> 615243, which cycles after 6 iterations.
This appears to coincide with the numbers n such that a type-2 optimal normal basis exists for GF(2^n) over GF(2). But are these two sequences really the same? - Joerg Arndt, Feb 11 2008. Comment from Jean-Guillaume Dumas (Jean-Guillaume.Dumas(AT)imag.fr), Mar 20 2008: The asnwer is Yes - see Theorem 2 of the Dumas reference.
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REFERENCES
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M. Bringer, Sur un probleme de R. Queneau, Math. Sci. Humaines No 25 (1969) 13-20.
Jacques Roubaud, Bibliotheque Oulipienne No 65 (1992) and 66 (1993).
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LINKS
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Joerg Arndt, Table of n, a(n) for n = 1..100
Joerg Arndt, draft of the fxtbook ("Algorithms for programmers").
Jean-Guillaume Dumas, Caracterisation des Quenines et leur representation spirale
G. Esposito-Farese, C program
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CROSSREFS
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Not to be confused with Queneau's "s-additive sequences", cf. A003044.
Sequence in context: A102825 A070991 A008747 this_sequence A070757 A123399 A104738
Adjacent sequences: A054636 A054637 A054638 this_sequence A054640 A054641 A054642
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KEYWORD
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nonn
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AUTHOR
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Gilles Esposito-Farese (gef(AT)cpt.univ-mrs.fr), May 17 2000
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EXTENSIONS
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Roubaud quotes the number 141, but the corresponding Queneau-Daniel permutation is only of order 47 = 141/3.
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