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Search: id:A071160
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| A071160 |
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Lukasiewicz words that are also valid asynchronic siteswap juggling patterns. |
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+0
3
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| 0, 1, 20, 11, 300, 201, 120, 111, 4000, 3001, 2020, 2011, 1300, 1201, 1120, 1111, 50000, 40001, 30020, 30011, 20300, 20201, 20120, 20111, 14000, 13001, 12020, 12011, 11300, 11201, 11120, 11111, 600000, 500001, 400020, 400011, 300300
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Note: this finite decimal representation works only up to the 511th term, as the 512th such word is already (10,0,0,0,0,0,0,0,0,0). The sequence A071161 shows the initial portion of this sequence sorted.
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LINKS
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Peter J. Beek and Arthur Lewbel, The Science of Juggling, Scientific American, Nov, 1995, Vol. 273, Number 5, pp. 92-97.
Joe Buhler and Ron Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
Juggling Information Service, Site Swap FAQs
A. Karttunen, Gatomorphisms and other excursions amidst the plane trees & parenthesizations (Includes the complete Scheme program for computing this sequence)
R. P. Stanley, Hipparchus, Plutarch, Schrö der and Hough, Am. Math. Monthly, Vol. 104, No. 4, p. 344, 1997.
Index entries for sequences related to Lukasiewicz words
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FORMULA
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Construction: starting from the most significant (the leftmost) bit, replace each 1-bit in the binary expansion of n with the distance to the next 1-bit to the right, allowing a cyclic wrap-over from the least-significant 1-bit to the most significant 1-bit. I.e. from 22 = 10110 in binary we get 20120, the 22nd term of this sequence.
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CROSSREFS
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A071160(n) = A071161(A054429(n)). Subset of A071153. A071162, A071163, Cf. also A060495, A060498, A065177.
Adjacent sequences: A071157 A071158 A071159 this_sequence A071161 A071162 A071163
Sequence in context: A033340 A040383 A058282 this_sequence A071153 A073868 A040382
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KEYWORD
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nonn,fini
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AUTHOR
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Antti Karttunen May 14 2002
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